Question

How do you solve the system of equations `-9x + 8y = 4` and `3x - 6y = - 18`?

Answer 1

Solution: `(4,5)`

Explanation:

Method: Eliminate the `x`'s in the equations, solve for `y`

Step 1. Make the 2nd equation have the same coefficient with opposite sign
`-9x+8y=4`
`3(3x-6y)=3(-18)` (multiply both sides by 3)

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`-9x+8y=4`
`9x-18y=-54`

Step 2. Add the two equations together
`-10y=-50`
`y=5` (divide both sides by `-10`)

Step 3. Determine the `x`-value by plugging this `y` back into one of the two originals

`-9x+8y=4`
`-9x+8(5)=4`
`-9x+40=4`
`-9x=-36`
`x=4`

Solution: `(4,5)`