Solving a system of linear equations when the lines are parallel

by RACHEL
(CALIFORNIA)

Find the value of k so that the two given lines will be parallel.

3X-KY=7
2X+5Y=-1

First, put the two equations in standard form

3X - KY = 7

3X - 7 = KY

3X/K -7/K = Y

Now put 2X + 5Y = -1 in standard form too

2X + 1 = -5Y

2X/-5 + 1/-5 = Y

The two equations are now in standard form
y = mx + b

3X/K -7/K = Y


2X/-5 + 1/-5 = Y

They are parallel if the slope are equal.

so they are parallel if 3/K = 2/-5

Cross multiply to get

2K = -15

so K = -15/2