Question

How do you solve the system of equations `10x-7y=-1` and `-2x-7y=-25`?

Answer 1

See a solution process below:

Explanation:

Step 1) Subtract the second equation:

`" "10x - 7y = -1`
`-(-2x - 7y = -25)`

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`10x - 7y = -1`
`""2x + 7y = 25`

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`12x + 0 = 24`

`12x = 24`

`(12x)/color(red)(12) = 24/color(red)(12)`

`(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = 2`

`x = 2`

Step 2) Substitute `2` for `x` in either of the equations and solve for `y`:

`10x - 7y = -1` becomes:

`(10 xx 2) - 7y = -1`

`20 - 7y = -1`

`-color(red)(20) + 20 - 7y = -color(red)(20) - 1`

`0 - 7y = -21`

`-7y = -21`

`(-7y)/color(red)(-7) = (-21)/color(red)(-7)`

`(color(red)(cancel(color(black)(-7)))y)/cancel(color(red)(-7)) = 3`

`y = 3`

The Solution Is: `x = 2` and `y = 3` or `(2, 3)`