Question

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).A coordinate grid with 2 lines. The first line passes through the points (negative 1.71, 0.14), (0, negative 1), and (3, negative 3). The second line passes through the points (negative 1.71, 0.14), (0, 1), and (2, 2).

Answer 1

We want the graph that shows y = (2/3)x + 1 and y = −(2/3)x − 1. Option C has the lines
- y = (2/3)x + 1 (passes through (0,1) and (3,3)), and
- y = −(2/3)x − 1 (passes through (0,−1) and (3,−3)).

They intersect at x = −1.5, y = 0, so the correct choice is Option C.