Question

Here is a linear equation in two variables: 2x+4y−31=123. Solve the equation, first for x and then for y.

Answer 1

`x = 77 - 2y`

`y = (77 - x)/(2)`

Explanation:

Given

`2x + 4y - 31 = 123`

Required

Solve for x and for y

`2x + 4y - 31 = 123`

Add 31 to both sides

`2x + 4y - 31+31 = 123+31`

`2x + 4y = 154`

Solving for x

Subtract 4y from both sides

`2x + 4y - 4y = 154 - 4y`

`2x = 154 - 4y`

Divide by 2

`x = 77 - 2y`

Solving for y

`2x + 4y = 154`

Subtract 2x from both sides

`2x - 2x + 4y = 154 - 2x`

`4y = 154 - 2x`

Divide by 4

`y = (154 - 2x)/(4)`

Split

`y = (77 - x)/(2)`