Question

How do you evaluate this system of equations: `y-2x=-5; y-x=-3`?

Answer 1

`x=2`, `y=-1`; Ordered Pair: `(2,-1)`

Explanation:

1. To solve this specific system, the easiest method is substitution.
   `y-2x=-5`
   `y-x=-3`
2. Choose one of the equations .. I will pick `y-x=-3`.
3. The objective is to get one of the variables (`x` or `y`) by itself on one side of the equation .. Pick a variable to isolate .. I will pick `y`.
4. To isolate `y`, ADD `x` to both sides of the equation:
   `y-x=-3`
   `y=-3+x`
5. Look at the OTHER equation (the one you did not choose) .. That would be `y-2x=-5` for me.
   See how `y` is EQUAL to `(-3+x)` ?
   You can substitute the `y` in `y-2x=-5` with `(-3+x)`
   It should look like this: `(-3+x)-2x=-5`
6. SIMPLIFY! Now we only have ONE variable in the equation.
   `(-3+x)-2x=-5`
   `-3-x=-5`
   `-x=-2`
   `x=2` [THIS IS THE ANSWER FOR X]
7. Take one of the equations and substitute `x` for `2` to solve for `y`.
   `y-2x=-5`
   `y-2(2)=-5`
   `y-4=-5`
   `y=-1` [THIS IS THE ANSWER FOR Y]

If your teacher wants it as `(x,y)`, it is `(2,-1)`.