Question

What are x and y if `7x+5y=18` and `-7x-9y=4`?

Answer 1

`(x,y) = (6 13/14, -5 1/2)`
`color(white)("XXX")`This may be wrong if I changed the first expression into the wrong equation, but it was meaningless as written

Explanation:

[1]`color(white)("XXX")7x+5y=18color(white)("XXXXXX")`note: I changed this from original version `7x+5y+18`
[2]`color(white)("XXX")-7x-9y=4`

Adding [1] and [2]
[3]`color(white)("XXX")-4y = 22`

Dividing both sides by `(-4)`
[4]`color(white)("XXX")y = -5 1/2`

Substituting `(-5 1/2)` for `y` in [1]
[5]`color(white)("XXX")7x+5(-5 1/2) =18`

Simplifying
[6]`color(white)("XXX")7x-27 1/2 = 18`

[7]`color(white)("XXX")7x = 45 1/2`

[8]`color(white)("XXX")x= 6 13/14`

Answer 2

`x=13/2`
`y =(-11)/2`

Explanation:

`7x+5y=18`----------------(1)
`-7x-9y=4`-----------------(2)

Since the co-efficients of `x` is `7` and `-7`, we can eliminate `x` by adding the two equations.

`7x+5y=18`----------------(1) ADD with (2)
`-7x-9y=4`-----------------(2)

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`-4y=22`
`y =22/(-4)=(-22)/4=(-11)/2`
`y =(-11)/2`

Substitute `y =(-11)/2` in equation (1)

`7x +5((-11)/2)=18`
`7x -55/2=18` Multiply both sides by 2
`14x-55=36`
`14x=36+55`
`14x=91`
`x=91/14=13/2`
`x=13/2`