Question

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

Answer 1

Solving using substitution

Explanation:

2x + y = -5
y = -5 - 2x
3x - 5(-5 - 2x) = 2
3x + 25 + 10x = 2
13x = 2 - 25
13x = -23
x = `-23/13`

Substitute `-23/13` for x.

2(`-23/13`) + y = -5
`-46/13` + y = -5
y = `-19/13`

The solution set is (`-23/13`, `-19/13`).

Below are a few exercises to practice yourself. At the end, I put a linear-quadratic system a for a little bit of a challenge should you want it... Be warned of more than one solution set in the linear-quadratic system. Feel free to ask for help with the linear-quadratic system.

a) 2x + 3y = 6
x - 5y = -11

b) 4x - 7y = -12
2x - 14y = 3

c) `x^2` + 12x = -y - 13
-2x - y = 4

Enjoy!