How do you solve the following system?: 12x+7y=3,4x+3y=2

1 Answer
Nov 13, 2015

x=2.875
y=4.5

Explanation:

We start with:
12x+7y=3,
4x+3y=2.

There are (as far as I know) three methods of solving simultaneous equations. I'll choose substitution. Therefore we must leave either x or y alone. I'll choose x in the second equation (you can choose any of the 2 variables in any of the 2 equations):
4x+3y=2,
4x=3y2,
x=3y24.

We now substitute x in the other equation such that:
12x+7y=3,
12(3y24)+7y=3, 12 and 4 cancel out,
3(3y2)+7y=3,
9y6+7y=3, we now add ys and pass the 6 to the other side,
2y=9,
2y=9,
y=4.5.

We now substitute y by this value in any of the 2 equations. I'll choose the second one:
4x+3(4.5)=2,
4x13.5=2, we now pass 13.5 to the other side,
4x=11.5,
x=2.875.

Hope it Helps! :D .