Question

Solve the linear system of equations using addition. Graph the equations to verify your solution.
{-4x = y + 3
{y = -4x - 3



WRITER

Answer 1

First rewrite both equations in standard form.

From -4x = y + 3: -4x - y = 3.
From y = -4x - 3: 4x + y = -3.

Add the two equations:
(-4x - y) + (4x + y) = 3 + (−3)
0 = 0.

This identity shows the two equations are dependent (they are the same line). So there are infinitely many solutions: every point on the line y = −4x − 3 is a solution. You can parametrize them by x = t, y = −4t − 3 (t any real number).

To verify by graphing: both equations graph to the same line with slope −4 and y-intercept −3. Example points on the line: (0, −3), (1, −7), (−1, 1).