Given the system of linear equations Part A: Graph the system of linear equations. Part B: Use the graph created in Part A to determine the solution to the system. Part C: Algebraically verify the solution from Part B.

We have:

The system of linear equations:

x+6y=6

y=1/3 x−2

Part A: Graph is shown in the picture.

Part B: The intersection point is (6, 0)

x = 6

y =0

Part C: By substitution method.

x  = 6

y = 0

Thus, the solution to the system of linear equations x+6y=6 and y=1/3 x−2 is x = 6 and y = 0.

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The graph of the system of linear equations is represented below.

The solution for the equations x+6y=6 and y= 1/3 x - 2 are x = 6 and y = 0.

A set of variables called an equation is one in which two mathematical expressions are equivalent to one another.

The given system of linear equations,

x+6y=6              (1)

And, y= 1/3 x - 2       (2)

Part A : The graph of the equations shown below:

Part B :

The lines intersect each other at (6, 0)

Therefore, the solution for the equations are x = 6 and y = 0.

Part C:

Substitute the value of x= 6 in the equation (1),

6 + 6y = 6

y = 0.

Also substitute the value of x = 6 in equation (2)

y = (1/3)x6 - 2

y = 2 - 2

y = 0

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