How do you solve the system of equations #2x + y = 30# and #4x + 2y = 60#?

1 Answer
Apr 13, 2018

An infinite number of solutions exist.

Explanation:

We can start by using substitution.
The first equation solves easily for #y#, so just subtract #2x# from both sides:
#y=-2x+30#

This equals "#y#". Plug in this expression for #y# in the second equation and solve for #x#:
#4x+2(-2x+30)=60#
#4x-4x+60=60#
#0=0#

But wait- the "#x#"s cancel out! What does that mean? Well, there are an infinite number of solutions to this system- so you can't just find one "#x=#" and "#y=#".
So that's the answer: There are an infinite number of solutions.

Also, you can try dividing both sides of the second equation by #2#:
#2x+y=30#, which is actually the exact same line as the first one. When the equations in
a given system of equations represent the same line, it is called a dependent system.