Question

How do you find an ordered pair for `-7x + 6y = 11 and 8x - 3y = -1`?

Answer 1

`x=1 and y=3`
`(1,3)`

Explanation:

"Find an ordered pair" means find `(x,y)`, which in other words means, solve the system of equations.

The ideal situation is to have one of the variables in the two equations as additive inverses.
Notice that the `y`-terms already have opposite signs.

`-7x color(blue)(+ 6y) = 11 and 8x color(blue)(- 3y) = -1`

Multipying the second equation by `2` will give `-6y`

`color(white)(..............)-7x + 6y =" " 11`......................A
`color(white)(...................)8x -3y = -1`.......................B

`B xx2:color(white)(.....)16x - 6y = -2`......................C
`color(white)(..............)-7x + 6y =" " 11`......................A

`A+C:color(white)(.....)9x =9`
`A+C:color(white)(......)x = 1`

Substitute #x=1 into A (or any other equation.

`-7(1) + 6y = 11`

`6y= 11+7`
`6y = 18`
`y =3`

Check in B:

Is `8(1) -3(3) = -1`?
`" "8 -9`
`= -1`
.