Question

How do solve the following linear system?: `3x + y =20 , -3x -8y = -9`?

Answer 1

`x=(151/21)` and `y=(-11/7)` or in other words the solution is the ordered pair `(151/21,-11/7)`

Explanation:

We will use the "Elimination Method" to help us start to solve this problem. I can easily eliminate the `x` variable by addind the two equations:
`3x+y =20`
`-3x-8y=-9` by adding like terms we get:

`-7y =11`
`y =-11/7`
Now that I have a value for `y`, I will substitute that in the first equation and solve for `x`
`3x+y=20`
`3x +(-11/7) = 20`
`3x = 20+11/7` I need a common denominator, which is `7`
`3x = 140/7 + 11/7`
`3x=151/7` Divide both sides of the equation by `3`
`x=151/21`