Question

Do you need to add or subtract the equations `5x+7y=-31` and `5x-9y=17` to solve the system?

Answer 1

See answer below

Explanation:

Given: `5x + 7y = -31; " and " 5x -9y = 17`

Since both equations have a `5x`, subtract one from the other to eliminate the `x` terms:

`" "5x + 7y = -31`
`ul(-(5x -9y = " "17" "))`
`" " 16y = -48; " "y = -48/16 = -3`

Substitute this value for `y` in either of the equations to find the value of `x`:

`5x +7(-3) = -31`

`5x -21 = -31`

Add `21` to both sides: `" "5x = -31 + 21 = -10`

`x = -10/5 = -2`

Check your answer by substituting both `x` and `y` into the other equation:

`5(-2) - 9(-3) = 17`

`-10 +27 = 17`, which is TRUE

Solution: is a point (-2, -3)
which is the intersection point common to both lines