Questions: Solve the system of linear equations by graphing. x - 4y = 12 5x + 4y = -12

Solution Steps

The given system of linear equations is: \[ x - 4y = 12 \] \[ 5x + 4y = -12 \]

First, we need to convert these equations into slope-intercept form \( y = mx + b \).

For the first equation: \[ x - 4y = 12 \] \[ -4y = -x + 12 \] \[ y = \frac{1}{4}x - 3 \]

For the second equation: \[ 5x + 4y = -12 \] \[ 4y = -5x - 12 \] \[ y = -\frac{5}{4}x - 3 \]

Next, we graph the two equations on the same coordinate plane.

1. For \( y = \frac{1}{4}x - 3 \):

   • The y-intercept is -3.
   • The slope is \(\frac{1}{4}\), so for every 4 units you move to the right, you move 1 unit up.

2. For \( y = -\frac{5}{4}x - 3 \):

   • The y-intercept is -3.
   • The slope is \(-\frac{5}{4}\), so for every 4 units you move to the right, you move 5 units down.

The solution to the system of equations is the point where the two lines intersect.

By graphing the equations, we observe that both lines intersect at the point \((0, -3)\).

Final Answer