Question

Solve the system of equations -4x+5y=64−4x+5y=64 and -x+y=12−x+y=12 by combining the equations.

Answer 1

`x=4`

`y=16`

Explanation:

Given system of equations:

A)
`-4x+5y=64`

B)
`-x+y=12`

Solving the system by combining the equations.

Rearranging equation B, to solve for
`y` in terms of
`x`

Adding both sides by
`x`

`-x+y+x=12+x`

`y=12+x`

Combining equations by substituting rearranged equation B into equation A in place of
`y`.

`-4x+5(12+x)=64`

Using distribution.

`-4x+60+5x=64`

Simplifying.

`x+60=131`

Subtracting both sides by 60.

`x+60-60=64-60`

∴
`x=4` (Answer)

We can plugin
`x=4` in the rearranged equation B to get value of
`y`

`y=12+4`

∴
`y=16` (Answer)