# How do you solve the following system: #x-4y=2, 5x+2y=20 #?

##### 1 Answer

Jan 18, 2016

#### Explanation:

Take the first equation.

#x-4y=2#

Add

#x=4y+2#

Since we know that

#5color(red)x+2y=20#

#5color(red)((4y+2))+2y=20#

Distribute and solve for

#20y+10+2y=20#

#22y=10#

#y=10/22=5/11#

Now that we know the value for

#x-4color(blue)y=2#

#x-4color(blue)((5/11))=2#

#x-20/11=2#

#x=22/11+20/11=42/11#

Since

We can check a graph:

graph{(x-4y-2)(5x+2y-20)=0 [-5.26, 10.54, -3.38, 4.516]}