Question

What is the solution to the system of equations?
x-2y=-8
4x-8y=10

Answer 1

The equations are parallel! There is no solution.

Explanation:

Our equations are:

#1 x-2y=-8

#2 4x-8y=10

The first step is to see if it is possible to simplify either of the equations, which is possible for equation #2.

4x-8y=10 -> 2x-4y=5

#2 is now 2x-4y=5

Next, we must compare the slopes of the equations. If they are parallel, substitution or adding/subtraction methods for a system of equations will not work. Each equation will now be put into slope-intercept form; y=mx+b, where m equals the slope and b is the y intercept.

#1

x-2y=-8

`(1)/(2) x=y-4\\\\-y=(-1)/(2)x-4\\\\y=(1)/(2)x+4`

#2

2x-4y=5

`2x-4y=5\\2x=5+4y\\(2x)/(4)=(5+4y)/(4) \\(1)/(2)x=(5)/(4)+y \\\\\\frac{1}{2}x-(5)/(4)=y\\y=(1)/(2)x-(5)/(4)`