Question

How do you solve the following system: `5x-9y=-2, 7x-2y= -67`?

Answer 1

`(x,y)=( -11 16/53,-6 3/53)`

Explanation:

Given
[1]`color(white)("XXX")5x-9y=-2`
[2]`color(white)("XXX")7x-2y=-67`

Convert to equivalent equations with the same coefficient for `y`
by multiplying [1] by `2`
and multiplying [2] by `9`
[3]`color(white)("XXX")10x-18y=-4`
[4]`color(white)("XXX")63x-18y=-603`

Subtract [3] from [4] to eliminate the `y` term
[5]`color(white)("XXX")53x=-599`

Divide both sides of [5] by `53`
[6]`color(white)("XXX")x=-599/53= -11 16/53`

We could substitute `-599/53` for `x` in one of the given equation (either one) and solve for `y`
or repeat a similar process to the one above to eliminate the `x` factors:

Multiply [1] by `7` and [2] by `5`
[7]`color(white)("XXX")35x-63y=-14`
[8]`color(white)("XXX")35x-10y=-335`

Subtract [7] from [8]
[9]`color(white)("XXX")53y=-321`

Divide both sides of [9} by `53`
[10]`color(white)("XXX")y=-321/53=-6 3/53`