Question

How do I use substitution to find the solution of the system of equations `y=1/3x+7/3` and `y=-5/4x+11/4`?

Answer 1

In this problem we have 2 different expressions that represent the value of `y`. Because they both represent `y` we can set them equal to each other.

`(1/3)x+7/3=-(5/4)x+11/4`

Because all of the terms share a common multiple of 12 I will multiply each term by 12 to eliminate the fractions.

`12[(1/3)x+7/3=-(5/4)x+11/4]`

`[(12/3)x+84/3=-(60/4)x+132/4]`

`4x+28=-15x+33`

`19x=5`

`x=5/19`

Substitute in this newly found `x`-value into one of the original equations.

`y=(1/3)x+7/3`

`y=(1/3)*(5/19)+7/3`

`y=(5/57)+7/3*19/19`

`y=5/57+133/57`

`y=138/57`

`y=46/19`