Question

How do you solve the system of equations `2x - 3y = - 1` and `- 4x + 5y = - 3`?

Answer 1

`x = 7`
`y = 5`

Explanation:

`color(white)(...)` `2x−3y=−1`
`−4x+5y=−3`

If you multiply the first equation by `-2`, the coefficients of the `x` terms in both equations will be the same.

Then you can eliminate the `x` terms by subtracting one equation from the other so that the `x` terms go to zero.

Then it's easy to solve an equation in a single unknown.

`color(white)(....................)`. . . . . . . . . . . . .

1) Multiply all the terms on both sides of the first equation by `-2` to make the coefficients of the `x` terms the same.
After you multiply, you will get this:
`-4x+6y=2`

2) Subtract one of the equations from the other to make the `x` terms drop out
`color(white)(....)`(`-4x+6y=  2`)
`-`(`−4x+5y=` `"-"` `3`)

3) Clear the parentheses by distributing the minus sign
`-4x+6y=2`
`+4x-5y=3`

4) Add the equations and let the `x` terms go to 0
`y = 5` `larr` answer for `y`

`color(white)(....................)`. . . . . . . . . . . . .

Use the value (`y = 5`) to find the value of `x`

1) Sub in `5` in the place of `y` in one of the equations
`2x−3 (y)=−1`
`2x−3 (5)=−1`

2) Clear the parentheses
`2x - 15 = - 1`

3) Add `15` to both sides to isolate the `2x` term
`2x = 14`

4) Divide both sides by `2` to isolate `x`
`x = 7` `larr` answer for `x`

Answer:
`x = 7`
`y = 5`