Question

How do you find the solution of the system of equations `x+2y=5` and `2x-3y=-4`?

Answer 1

The answer is `x=5-2y` and `y=2`

Problem: Solve the system of equations `x+2y=5` and `2x-3y=-4`.

First equation. Solve for `x`.

`x+2y=5`

Subtract `2y` from both sides.

`x=5-2y`

Second equation. Solve for `y`.

Substitute `5-2y` for `x` in the other equation. Solve for `y`.

`2x-3y=-4` =

`2(5-2y)-3y=-4`

Distribute the `2`.

`10-4y-3y=-4`

Combine like terms.

`-7y+10=-4` =

`-7y=-14`

Divide both sides by `-7`.

`y=2`

Check your answers by substituting the values for `x` and `y` back into both of the original equations.

`x+2y=5` =

`5-2*2+2*2=5` =

`5-4+4=5` =

`5=5`

`2x-3y=-4` =

`2(5-2*2)-3*2=-4`

Distribute the `2`.

`10-8-6=-4` =

`-4=-4`

The answers check!