Question

How do you solve -10x + y = 0 and 5x + 3y = -7?

Answer 1

`{(x = -1/5), (y = -2):}`

Explanation:

Your starting system of equations looks like this

`{(-10x + y = 0), (5x + 3y = -7):}`

Multiply the second equation by `2` to get

`{(-10x + y = 0), (10x + 6y = -14):}`

If you add these equations by adding the left-hand side and the right-hand side separately, you can eliminate the `x`-term.

The resulting equation will only have one unknown, `y`.

`{(-10x + y = 0), (10x + 6y = -14):}`
`stackrel("-------------------------------------------")`
`-color(red)(cancel(color(black)(10x))) + y + color(red)(cancel(color(black)(10x))) + 6y = 0 + (-14)`

`7y = -14 implies y = (-14)/7 = color(green)(-2)`

Pick one of the original equations and substitute `y` with the value you've just calculated to get the value of `x`

`-10x + (-2) = 0`

`-10x = 2 implies x = color(green)(-1/5)`