Solve the system of equations by graphing.

Question

5x-4y=-24, 5x=4y-24?

Answer 1

The system of equations are 5x - 4y = - 24 and 5x = 4y - 24

Write the equations in slope-intercept form y = mx + b, where m is slope and b is y -intercept.

First equation is 5x - 4y = - 24

y = (-5x)/(-4) + 6 ---> (1)

Second equation is 5x = 4y - 24

y = 5x/4 + 6 ---> (2)

Observe the two equations are equal.

Graph the two lines.

First line y = (-5x)/(-4) + 6

Slope = -5/-4 and y-intercept is 6.

y-intercept is 6, so the line crosses the y-axis at (0,6)

Using slope find the next point.

Slope = rise/run = -5/-4

Start at point (0, 6), move 5 down and 4 units left, then plot the point (-4, 1).

Draw a line through these points

Second line y = 5x/4 + 6

Slope = 5/4 and y-intercept is 6.

y-intercept is 6, so the line crosses the y-axis at (0,6)

Using slope find the next point.

Slope = rise/run = 5/4

Start at point (0, 6), move 5 up and 4 units right, then plot the point (4, 11).

Draw a line through these points.

Observe the two lines are coincident.

There are infinitely many solutions.