Question

How do you solve 3u + z = 15 and u + 2z = 10?

Answer 1

`{(u=4), (z=3) :}`

Explanation:

Your system of equations looks like this

`{(3u+z = 15), (u + 2z = 10):}`

Multiply the first equation by `(-2)` to get

`{(3u+z = 15 | * (-2)), (u + 2z = 10):}`

`{(-6u-2z = -30), (u + 2z = 10):}`

Add these two equations to get one equation with one unknown, `u`

`-6u - color(red)(cancel(color(black)(2z))) + u + color(red)(cancel(color(black)(2z))) = -30 + 10`

`-5u = -20 implies u = ((-20))/((-5)) = color(green)(4)`

Now use this value of `u` in one of the wo original equations to find `z`

`4 + 2z = 10`

`2x = 6 implies z = 6/2 = color(green)(3)`