Solve the system of linear equations by substitution. Check your solution.

Answer:

[tex]x = 1.5[/tex]

[tex]y =1[/tex]

Step-by-step explanation:

Given

[tex]4x + 2y = 8[/tex]

[tex]6x - 4y = 5[/tex]

Required

Solve for x and y

[tex]4x + 2y = 8[/tex] --- (1)

[tex]6x - 4y = 5[/tex] --- (2)

Divide equation (1) through by 2

[tex]\frac{1}{2}(4x + 2y) = 8*\frac{1}{2}[/tex]

[tex]2x + y = 4[/tex]

Make y the subject

[tex]y = 4 - 2x[/tex]

Substitute 4 - 2x for y in equation (2)

[tex]6x - 4y = 5[/tex]

[tex]6x - 4(4- 2x) = 5[/tex]

Open bracket

[tex]6x - 16+ 8x = 5[/tex]

Collect Like Terms

[tex]6x + 8x = 5+16[/tex]

[tex]14x = 21[/tex]

Solve for x

[tex]x = \frac{21}{14}[/tex]

[tex]x = 1.5[/tex]

Substitute 1.5 for x in [tex]y = 4 - 2x[/tex]

[tex]y = 4 - 2(1.5)[/tex]

[tex]y = 4 - 3[/tex]

[tex]y =1[/tex]

To check the solution:

Substitute the values of x and y i the equations

[tex]4x + 2y = 8[/tex]

[tex]4 * 1.5 + 2 * 1 = 8[/tex]

[tex]8 = 8[/tex]

[tex]6x - 4y = 5[/tex]

[tex]6 * 1.5 - 4 * 1 = 5[/tex]

[tex]5 = 5[/tex]

Hence, the solution is true

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