Solving Systems of Linear Equations: Graphing — Quiz

Question 7 • Algebra I

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 first line passes through the points (negative 1.7 comma 1.57), (0 comma negative 1), and (2 comma negative 4). The second line passes through the points (negative 1.7 comma 1.57), (0 comma 1), and (3 comma 0).

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

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

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

Explanation

The equations have y-intercepts 1 and −1, so the graph should show one line crossing the y-axis at (0, 1) and the other at (0, −1). Set the equations equal to find where they intersect: (2/3)x + 1 = −(2/3)x − 1, which gives x = −1.5 and y = 0. Choice B shows both intercepts and the intersection at (−1.5, 0).

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