Solve by substitution

Question

X+y=10

y=2x^2

Answer 1

Hello Tracy,

 

To solve this, we can either isolate x or y in the first equation or the second. Since y is already by itself in the second equation, I'll use that substitution.

 

We plug 2x² into our first equation in place of y to get x+2x²=10 --> 2x²+x-10=0 --> (2x+5)(x-2)=0 

--> 2x+5=0 or x-2=0 (by the zero product property) --> x=-5/2 and/or x=2

 

We check both of these in both equations: 

x=-5/2 gives us -5/2+y=10--> y=10+5/2=25/2 in equation 1 and y=2(-5/2)²=2(25/4)=25/2 in equation 2, so x=-5/2 works for both!

 

x=2 gives us 2+y=10 --> y=10-2=8 in equation 1 and y=2(2)²=2(4)=8 in equation 2, so x=2 works for both!

 

Thus, we have (-5/2, 25/2) and (2, 8) as possible sets of solutions for this problem. 

 

A little long, but I hope that helped. 

 

Matt