Question

How do you solve 5x + y = -2 and 4x + 7y = 2?

Answer 1

`{(x = -16/31), (y = 18/31) :}`

Explanation:

Take a look at your system of equations

`{(5x + y = -2), (4x+7y = 2) :}`

Notice that if you multiply the first equation by `(-7)` and add the left-hands sides and the right-hand sides of the two equations, you can eliminate the `y`-term.

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

`{(5x + y = -2 | * (-7)), (4x+7y = 2) :}`

`{(-35x -7y = 14), (4x+7y = 2) :}`
`stackrel("-----------------------------------------------")`

`-35x - color(red)(cancel(color(black)(7y))) + 4x + color(red)(cancel(color(black)(7y))) = 14 + 2`

`-31x = 16 implies x = 16/((-31)) = color(green)(-16/31)`

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

`5 * (-16)/31 + y = -2`

`y = -2 + 80/31`

`y = color(green)(18/31)`