Question

A pair of equations is shown below.

y = -6x - 3

y = -x + 2


Part A: Solve the system of equations using a graph, substitution, or elimination. Show or explain everything you did to find the solution.

Part B: Explain what the solution represents.

Answer 1

• A. (-1, 3)
• B. The intersection point of the two lines

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Part A

To solve the given system of equations, we can use either the substitution or the elimination method.

The first equation is:

• y = -6x - 3

The second equation is:

• y = -x + 2

Since both equations equal y, we can set them equal to each other:

• -6x - 3 = -x + 2

Solve it for x:

• -3 = 5x + 2
• -5 = 5x
• x = -1

Substitute x = -1 into either equation to find y. We will use the second equation:

• y = -(-1) + 2
• y = 1 + 2
• y = 3

The solution to the system of equations is (x, y) = (-1, 3).

Part B

The solution represents the point where the two lines intersect. In a graph, this point is where the lines cross each other, indicating the only pair of values of x and y that satisfy both equations simultaneously.