Question

How do solve the following linear system?: `-x+3y=-5 , 2x+7=-5y`?

Answer 1

I have taken you to a point where you can solve for `x`
`color(red)(y=-17/11)`

Explanation:

Given:
`-x+3y= -5` ...............................(1)
`2x+7=-5y`.................................(2)

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To solve a single equation you can only do so it contains only one unknown. So to solve any of these two we need to 'get rid of a variable'

Look at equation (1). We have a single `x`. So this is the simpler of the two to use as a source of values for substitution.

`color(blue)("Solving for y")`

Consider equation (1)

Multiply by (-1) to make the `x` positive

`x-3y=+5`

Add `3y` to both sides

`color(green)(x=3y+5)" "............................(1_a)`

Substitute for `x` in equation (2) using equation `(1_a)`

`color(brown)(2x+7=-5y" "color(blue)(->" "2(color(green)(3y+5))+7=-5y)`

`6y+10+7=-5y`

`6y+5y=-17`

`color(red)(y=-17/11)` ...................................(3)
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Substitute equation (3) into equation (1) or (2). You chose!

I will let you finish this off.