Question

Question #7659b

Answer 1

`x=-1 and y=-9`

Explanation:

One can solve this problem using substitution or elimination. Elimination is the better choice in this situation but in some cases one should use substitution.

Elimination Method
First convert both equations into standard form. `(Ax + By = C)`

`7x-3y=20" and "y=5x-4`

Move `5x` to the other side by subtracting `5x` from both sides:

`7x-3y=20" and "-5x+ y=-4`

Next eliminate one of the variables by making the " x " or " y " equal to cancel each other out by subtraction.

In this case it's better to eliminate the " y " variable.
To eliminate the " y " variable, multiply the lower equation
`(-5x+ y=-4)` by `3` so the " y " terms are equal.

However, one of the " y "s must be negative so they can cancel each other out .

`7x-3y=20" and 3(-5x+ y=-4)`

`" "7x-3y=20`
`-15x+3y=-12`

Add the two equations. The " y " terms will cancel out.

`-8x=8" "` Divide both sides by `-8` to isolate the variable.

`x=-1`

But, you're not done yet! You have only solved for " x. "
You still have to solve for the " y " variable.

This part is simple. Just plug in the `x=-1` into either of the two original equations.

For an example plug in `x=-1" into " 7x-3y=20`

`7(-1)-3y=20`
`-7-3y=20`

Isolate the variable but adding `7` to both sides.

`-3y=27" "` Divide by `-3`
`y=-9`