Sylvie finds the solution to the system of equations by graphing.

y = A system of equations. y equals StartFraction 2 over 3 EndFraction x plus 1. y equals negative StartFraction 2 over 3 EndFraction x minus 1x + 1 and y = x – 1

Which graph shows the solution to Sylvie’s system of equations?

A coordinate grid with 2 lines. The first line passes through the points (negative 1.7, 1.57), (0, negative 1), and (2, negative 4). The second line passes through the points (negative 1.7, 1.57), (0, 1), and (3, 0).

A coordinate grid with 2 lines. The first line passes through the points (negative 1.02, 0.63), (0, negative 1), and (2, negative 4). The second line passes through the points (negative 1.02, 0.63), (0, 1), and (3, 2).

A coordinate grid with 2 lines. The first line passes through the points (negative 1.5, 0), (0, negative 1), and (3, negative 3). The second line passes through the points (negative 1.5, 0), (0, 1), and (3, 3).

The solution to a system of linear equations is the point where the two graphs intersect. The coordinates of that point is the solution.

Given the system as:

y = 2/3x + 1

y = -2/3x - 1

Add both together to eliminate x

2y = 0

y = 0

Substitute y = 0 into y = 2/3x + 1 to find x

0 = 2/3x + 1

-1 = 2/3x

-3 = 2x

-3/2 = x

x = -3/2

The solution is: (-3/2, 0) = (-1.5, 0).

Therefore, the graph that shows the solution will intersect at (-1.5, 0), which is shown in the image attached below.

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