Question

How do you solve this system of equations: `2x + y = - 2 and 5x + 3y = - 8`?

Answer 1

x = 2
y = -6

Explanation:

The question is asking to solve for 2 unknowns using 2 equations.

Let's start by rearranging one of the equation. That will make it easier to substitute. You can start with either equation, but I find the first equation easier to rearrange:
`2x + y = -2`
`2x + y color(red)( -2x) = -2 color(red)(-2x)` [move 2x to the other side]
`y = -2 -2x` [simplify]

and insert that into the second equation:
`5x + 3y = -8`
`5x + 3(color(red)(-2-2x))=-8` [substitute "-2-2x" for y]
`5x + color(red)(-6 -6x) = -8` [multiply out]
`-6 - x = -8` [simplify]
`x = 2`

Now that we have found the value for x, we can substitute in the value for x in any one of the equation to find the value for y.
`y = -2 -2x`
`y = -2 -2(2)` [substitute in the value of x]
`y = -6`