Question

How do you solve this system of equations: `x+ 3y = - 4 and 5x + 4y = 13`?

Answer 1

Solve for either x or y and substitute the value of the variable in the other equation to solve for which variable is left.

Explanation:

`x+3y = -4`

`5x +4y = 13`

I will Solve for `x` first because I see smaller numbers that are easier to deal with.

`x + 3y = - 4`

subtract `3y` from both sides to get `x` isolated

`x = -4 - 3y`

take this solution and plug it in for `x` in the other equation

`5(-4 - 3y) + 4y = 13`

distributive property

`-20 -15y + 4y = 13`

add like terms

`-20-11y = 13`

add `20` to both sides to isolate y

`-11y = 33`

divide both sides by a form of one to Isolate variable further

`(-11y)/-11 = 33/-11`

`y = -3`

for `x=-4-3y` substitute `y` to get `x`

`-4-3(-3) = 5`

the solutions to this system of equations are

`x=5`
`y=-3`