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Question 8 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY

Sylvie finds the solution to the system of equations by graphing. y is equal to 2 thirds x plus 1 and y is equal to negative 2 thirds x minus 1 Which graph shows the solution to Sylvie’s system of equations?

Answer

Image with description A coordinate grid with 2 lines. The x and y-axes are labeled from negative 5 to 5 in increments of 1. The first line passes through the points negative 1 point 0 2 comma 0 point 6 3, 0 comma negative 1, and 2 comma negative 4. The second line passes through the points negative 1 point 0 2 comma 0 point 6 3, 0 comma 1, and 3 comma 2.

Image with description A coordinate grid with 2 lines. The x and y-axes are labeled from negative 5 to 5 in increments of 1. The first line passes through the points negative 1 point 7 comma 1 point 5 7, 0 comma 1, and 3 comma 0. The second line passes through the points negative 1 point 7 comma 1 point 5 7, 0 comma negative 1, and 2 comma negative 4.

Image with description A coordinate grid with 2 lines. The x and y-axes are labeled from negative 5 to 5 in increments of 1. The first line passes through the points negative 1 point 5 comma 0, 0 comma negative 1, and 3 comma negative 3. The second line passes through the points negative 1 point 5 comma 0, 0 comma 1, and 3 comma 3.

Image with description A coordinate grid with 2 lines. The x and y-axes are labeled from negative 5 to 5 in increments of 1. The first line passes through the points negative 1 point 7 1 comma 0 point 1 4, 0 comma negative 1, and 3 comma negative 3. The second line passes through the points negative 1 point 7 1 comma 0 point 1 4, 0 comma 1, and 2 comma 2.

Explanation

Set the two expressions for y equal: (2/3)x + 1 = −(2/3)x − 1. Solving gives (4/3)x = −2, so x = −1.5; substituting gives y = 0. The lines therefore intersect at (−1.5, 0), and choice C shows that intersection, with y-intercepts −1 and 1.

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