Question

What is the value of y in the solution to the system of equations?

1/3 x + 1/4y = 1
2x – 3y = –30

Answer 1

1 Solve for x in 1/3x+1/4y=1
X=3(1-y/4)

2 Substitute x=3(1-y/4) into 2x-3y=-30
6−9y/2 =−30

3 Solve for y in 6-9y/2=-30
y=8

4 Substitute y=8 into x=3(1-y/4)
x=−3

5 Therefore,
x=-3
y=8

Answer 2

`x=-3\\y=8`

Explanation:

Given is a system of equations in two variables x and y as

`(x)/(3) +(y)/(4) =1\\2x-3y =-30`

First we will remove the denominator in the equations by taking Lcd

Multiply I equation by 12

`4x+3y =12...iii`

Add the second equation with iii equation

We get
`6x = -18x=-3`

Substitute in II equation

`2(-3)-3y =-30\\y=8`

Solution set is

`x=-3\\y=8`