Question

How do you solve 5x + y = 9 and 10x - 7y =-18?

Answer 1

`{(x=1), (y=4) :}`

Explanation:

Take a look at your starting system of equations

`{(5x + y = 9), (10x - 7y = -18) :}`

Notice that if you multiply the first equation by `(-2)`, and add the right-hand sides and the left-hand sides of the equations separately, you can eliminate the `x`-term.

This will leave you with one equation with one unknown, `y`.

`{(5x + y = 9 | * (-2)), (10x - 7y = -18) :}`

`{(-10x -2y = -18), (10x - 7y = -18) :}`
`stackrel("---------------------------------------------------")`

`-color(red)(cancel(color(black)(10x))) - 2y + color(red)(cancel(color(black)(10x))) - 7y = -18 + (-18)`

`-9y = -36 implies y = ((-36))/((-9)) = color(green)(4)`

Now use this value of `y` in one of the two original equations to find the value of `x`

`5x + (4) = 9`

`5x = 5 implies x = 5/5 = color(green)(1)`