Question

What is the value of y in the solution to the following system of equations `5x-3y=-112, x-6y=-14`?

Answer 1

`y=-52/27`

Explanation:

To solve for an unknown you need to manipulate things so that you just 1 unknown

I chose to get rid of `x` as we need to have just the unknown of `y`

Given:

`5x-3y=-122" "..............................Equation(1)`
`color(white)(5)x-6y=-14" "...............................Equation(2)`
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Consider `Equation(2)`

Add `6y`to both sides giving:

`x=6y-14" "...............................Equation(3)`

Using equation(3) substitute for `x` in equation(1)

`color(green)(5color(red)(x)-3y=-122" "->" "5(color(red)(6y-14))-3y=-122`

`" "color(green)(30y-70-3y=-122)`

`" "color(green)(27y-70=-122)`

Add 70 to both sides
`" "color(green)(27y=-122+70`

`" "color(green)(27y=-52)`
Divide both sides by 27
`" "color(green)(y=-52/27)`