Question

How do you solve the following system: #-29=5y-3x, 5x+2y=12 #?

Answer 1

`x = 118/31` and `y = -109/31`

Explanation:

We can eliminate a variable by subtracting out an equation.

For example, let's take 3 times the second plus five times the first:

`3(5x+2y = 12) implies 15x + 6y = 36`
`5(-3x + 5y = -29) implies -15x + 25y = -145`
Adding them together,
`31y = -109 implies y = (-109)/31`

We can now plug this into our second equation from before and get `x`:
`5x + 2((-109)/31) = 12 implies 5x = 12 + 218/31 = 590/31`
`x = 118/31`

Thus we have our answer.