TOPIC: similtaneous linear equations

p1 + 2q = 3,
p - 2q = 3

Answers

Answer 1

Answer:

q-0

p-3

Step-by-step explanation:

there are two ways to solve elimination or substitution method I'll use the latter

so take the second equation and find an expression equal to p

p-2q=3

p=2q+3

substitute the above expression in the first equation

(2q+3)1+2q=3

open brackets

2q+3+2q=3

collect like terms

4q+3=3

solve

4q=0

q=0

substitute q in any equation you want I'll choose the second

p-(2×0)=3

p-0=3

p=3

Answer 2

Answer:

p = 3 ; q = 0

Step-by-step explanation:

In this linear pair of eqn. in 2 variables , they have a unique solution i.e. they will have only single solution . We know that

[tex]p + 2q=3[/tex] & also [tex]p -2q=3[/tex] . So, we can also equate them as :-

[tex]p + 2q = p-2q[/tex] (∵ Both the eqn. have 3 in their right hand side product )

Solving the eqn. gives,

[tex]=> 2q + 2q = p-p\\=> 4q=0\\=>q=0[/tex]

Putting the value of q in any one of the linear eqn gives ,

[tex]p+2q=3\\=> p+2(0)=3\\=>p+0=3\\=>p=3[/tex]


Related Questions

Christian's car used 15 gallons to travel 270 miles. How far can he travel on 11 gallons?

Answers

Answer:

198

Step-by-step explanation:

270/15 gives us 18, his miles per gallon. multiply that by 11, and you get 198.

find the value of f(3) for the function f(x)=-4(x+3) f(3)=

Answers

Answer:

-24

Step-by-step explanation:

Given function

f(x)= -4(x+3)

To find

f(3)=?

Solution

Substitute x with 3 in the equation to find f(3)

f(3) = -4(3+3) = -4*6 = -24

How do you solve 2 1/3 + 5y = 4

Answers

Answer:

Not sure but that's my answer

Please help me to prove this!​

Answers

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π                     →  A = π - (B + C)

                                                     → B + C = π - A

Use the Pythagorean Identity: cos² A + sin² A = 1   →  sin² A = 1 - cos² A

Use Double Angle Identities: cos 2A = 2 cos² A - 1 → cos² A = (cos 2A + 1)/2

                                             → cos A = 1 - 2 sin² (A/2)    

Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]

Use Cofunction Identities:  cos (π/2 - A) = sin (A)

                                             sin (π/2 - A) = cos A

                                             cos (-A) = cos (A)

Proof LHS → RHS:

[tex]\text{LHS:}\qquad \qquad \sin^2\bigg(\dfrac{B}{2}\bigg)+\sin^2 \bigg(\dfrac{C}{2}\bigg)-\sin^2\bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Pythagorean:}\qquad 1-\cos^2 \bigg(\dfrac{B}{2}\bigg)+1-\cos^2 \bigg(\dfrac{C}{2}\bigg)-\bigg[1-\cos^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\cos^2 \bigg(\dfrac{B}{2}\bigg)-\cos^2 \bigg(\dfrac{C}{2}\bigg)+\cos^2 \bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Double Angle:}\quad 1-\bigg(\dfrac{\cos(2\cdot \frac{B}{2})+1}{2}\bigg)-\bigg(\dfrac{\cos (2\cdot \frac{C}{2})+1}{2}\bigg)+\bigg(\dfrac{\cos (2\cdot \frac{A}{2})+1}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1-\dfrac{\cos B}{2}-\dfrac{1}{2}-\dfrac{\cos C}{2}-\dfrac{1}{2}+\dfrac{\cos A}{2}+\dfrac{1}{2}\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}[1-(\cos B+\cos C)+\cos A][/tex]

[tex]\text{Sum to Product:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]

[tex]\text{Given:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{\pi -A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]

[tex]\text{Cofunction:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]    

[tex]\text{Double Angle:}\qquad \dfrac{1}{2}\bigg[1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)+1-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg[2-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin^2 \bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Factor:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{A}{2}\bigg)\bigg][/tex]

[tex]\text{Given:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{\pi -(B+C)}{2}\bigg)\bigg][/tex]

[tex]\text{Cofunction:}\qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)+\cos \bigg(\dfrac{B+C}{2}\bigg)\bigg][/tex]

[tex]\text{Sum to Product:}\ 1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot 2 \cos \bigg(\dfrac{(B-C)+(B-C)}{2\cdot 2}\bigg)\cdot \cos \bigg(\dfrac{(B-C)-(B+C)}{2\cdot 2}\bigg)\\\\\\.\qquad \qquad \qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(-\dfrac{C}{2}\bigg)[/tex][tex]\text{Cofunction:}\qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{LHS = RHS:}\quad \checkmark\\\\\quad 1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)=1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)\quad[/tex]

                   

Melissa made a total of 14 baskets during her last basketball game. She made a number of 2-point baskets and a number of 3-point baskets for a total of 33 points. Using matrices to solve, how many 3-point baskets did Melissa make in her last basketball game? 3 5 9 11

Answers

Answer:

The answer should be 5

Step-by-step explanation: cause 3x5=15 which leaves 9 more shots that are equal to 2 2x9= 18 and 18+15= 33 which means the answer is 5

Answer:

B.) 5

Step-by-step explanation:

Edge2021

which expression is equivalent to 42+90?

Answers

Step-by-step explanation:

42+90 can be written in many ways.

Fore example, it can be written with double negatives, or even commutative property.

42-(-90) or 90+42

(21x2)+(45x2) or (6x7)+(3x30)

Sorry if it's wrong...

NEED HELP ASAP!!!
TEN POINTS!

Answers

The answer it’s letter D

9) What two operations are needed to solve 2x - 4 = 16?
a. Addition & division
b. Addition & subtraction
c.Multiplication & subtraction

Answers

Answer:

a. Addition & division

Step-by-step explanation:

2x - 4 = 16   (adding 4 to both sides)

2x  = 16 + 4

2x = 20  (dividing both sides by 2)

x = 20/2 = 10

Hence we can see that the two operations are addition and then division

Which of the following equations has been vertically stretched by a factor
of 5?
A) Y=|x+5|
B) Y=|x-5|
C) Y=5|x|

Answers

I think c because it’s talking about a factor

I need help ASAP PLEASE!
Determine whether this statement is true or false. If the statement is false, give a counterexample.
Statement: All integers are rational numbers.

Answers

heya....

your answer is:

All rational numbers are not integers. But all integers are rational numbers.

The statement is false.

It may help you...☺☺

a ball is thrown straight up from a height of 3 ft with a speed of 32 ft/s.

Answers

It was thrown about the length of 26ft

Point g is on line segment FH. Given FG=5x+2, GH= 3x-1, and FH= 9, determine the numerical length of FG.

Answers

Answer:

Step-by-step explanation: fg + Gh = fh

8x+1=9

8x=8

X=1

The numerical length of the line segment FG is 7 units.

Given that, FG=5x+2, GH= 3x-1, and FH= 9.

We need to find the numerical length of FG.

What is a line segment?

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.

Now, FH=FG+GH

⇒9=5x+2+3x-1

⇒8x+1=9

⇒8x=8

⇒x=1

So, FG=5x+2=7

Therefore, the numerical length of the line segment FG is 7 units.

To learn more about a line segment visit:

https://brainly.com/question/25727583.

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¿Cuál es el valor de 0.1561 redondeado a la décima más cercana?
A 0.15
B 0.16
C 0.1
D 0.2

Answers

Answer:

A0.15

Step-by-step explanation:

The function f is defined by the following rule.
f(x) = 3x - 3
Complete the function table,
X
- 4
2
5

Answers

X= -4; f(x)= -15
X= 2; f(x)= 3
X=5; f(x)= 12

If mZA = (8x + 6)° and m
ZB = (7x + 24)', then find the measure of ZB

Answers

i got x=18 i think u mistaken za for zb

can someone help me with this question? I keep on getting it wrong.

Answers

Answer:

102

Step-by-step explanation:

Let x be the amount of money John spends.

x/2-5=46

x/2=51

x=102

The ratio of dogs to cats is 3:8 there are a total of 99 dogs and cats in the shelter. How many are cats.

Answers

Answer:

72 cats

Step-by-step explanation:

sum the parts of the ratio, 3 + 8 = 11 parts

Divide the total by 11 to find the value of one part of the ratio.

99 ÷ 11 = 9 ← value of 1 part of the ratio, then

8 parts = 8 × 9 = 72 ← number of cats

3/5(1 + p) = 21/20
find the solution to p

Answers

Answer:

3/4

Step-by-step explanation:

3/5(1+p)-21/20

3/5+3/5p=21/20

3/5p=21/20-3/5

3/5p=21/20-12/20

3/5p=9/20

p=9/20÷3/5

p=9/20*5/3

p=45/60

p=3/4

2(3-p)=17=41 show answer.

Answers

this is what I found hope its correct!‍♀️

i have a zero in the ones place. i am greater than 20 but less the 39 what am i

Answers

Answer:

30

Step-by-step explanation:

A scale on a blue print drawing of a house shows that 10 centimeters represents 2 meters. What number of actual meters are represented by 18 centimeters on the blue print?

Answers

Answer:3.6 m

Given:10cm=2m

Then, 5cm=1m

Therefore, (18/5)= lenght I'm meters on blueprint scale

(18/5)=3.6m

Dominic placed the following pieces of lumber in order from shortest to longest 23 over three 7 and 7/8 7.9 to 68 square root

Answers

Answer:

23/3

7 7/8

7.9

Step-by-step explanation:

What is the unit rate (words per 1 minute) for
this scenario?



Lucy can type 300 words in 5 minutes. How many words can Lucy type in 27 minutes.

Answers

Answer: Lucy can type 1620 words in 27 minutes. She types 60 wpm, so you need to multiply 60x27 = 1620.

state the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation

Answers

Answer:

domain (-∞, ∞)range (-∞, 4]increasing (-∞, 0)decreasing (0, ∞)constant (only at x=0, not on any interval)

Step-by-step explanation:

The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).

The vertical extent of the graph includes y=4 and all numbers less than that:

  range: (-∞, 4]

The graph is increasing to the left of its vertex at x=0, decreasing to the right.

  increasing (-∞, 0); decreasing (0, ∞)

There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.

DOES ANYONE KNOW THIS?????

Answers

Answer:

if i;m right its 45 degrees

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

alternative angle theorem lets you know that angle acb is equal to cae and you can find acb since you know all angles add up to 180. 180-105-47=28

Hi May I know how to solve this question

Answers

The correct answer is (2) 150
(3) is the correct answer!

Kesha drives 26 miles in 48 minutes. Keeping the same rate, how many miles does she drive in 12 minutes

Answers

about 6.5 miles

this is because there will be about .54 miles in one minutes so then you multiply that by 12 and get about 6.5

hope that’s correct

5t+1= 9
Please help me​

Answers

Exact Form: t = 8/5

Decimal Form: t = 1.6

Mixed Number Form: t = 1 3/5 (one and three fifths)

Answer:

t = 8/5 or t = 1.6

This will be a fraction buh can be turned into a decimal

Step-by-step explanation:

subtract 1 on both sides 5t + 1 - 1 = 9 - 1

then simplify 5t = 8 after det divide both side 5t/5 = 8/5 and den your answer is t = 8/5...

HOPE DIS HELPS YU OR IS RIGHT!!!!!

if segment ac has a midpoint of b, and ab=32 and bc=5x+7, what is the length of segemnt bc

Answers

Answer:

             BC = 32

Step-by-step explanation:

B being midpoint of AC means:

BC = AB = 32

A pound is approximately 0.45 kilogram. A person weighs 87 kilograms. What is the person's weight, in pounds, when rounded to the nearest
whole number?
ОА
39 lb
OB. 52 lb
OC 193 lb
OD. 180 lb

Answers

Answer:

OC 193 lb is correcte!

The person's weight, in pounds, when rounded to the nearest

the whole number is equal to [tex]1.9\times10^{2} pound[/tex]

We have given that, A pound is approximately 0.45 kilogram.

0.45 kg = 1 pound

Thus if 0.45 kg is equal to= 1 pound

87 kg will be equal to [tex]=\frac{1}{0.45} \times 87=1.9 \times 10^2 pound[/tex]

What are the significant digits?

The number of significant digits in an answer should be equal to the least number of significant digits in any one of the numbers being multiplied, divided, etc.

Thus the answer should contain 2 significant digits.

To learn more significant digits visit:

https://brainly.com/question/24491627

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