Question

How do you solve `2x + 3y = -6` and `3x + 2y = 25`?

Answer 1

`color(red)("The solution is (5,-3).")`

One way is to use the method of elimination.

Step 1. Enter the equations.

[1] `3x+7y=-6`
[2] `x-2y=11`

Step 2. Multiply each equation by a number to get the lowest common multiple of the coefficients of one variable.

Multiply Equation 2 by `3`.

[3] `3x-6y =33`

Step 3. Subtract Equation 3 from Equation 1.

`3x+7y=color(white)(1)-6`
`3x-6y =" "33`
`stackrel(——————————)(" "color(white)(1)13y=-39)`

[4] `y = -3`

Step 4. Substitute Equation 4 in Equation 1.

`3x+7y=-6`
`3x+7(-3)= -6`
`3x-21=-6`
`3x=15`

`x=5`

Solution: The solution that satisfies both equations is `(5,-3)`.

Check: Substitute the values of `x` and `y` in Equation 2.

`x-2y=11`
`5-2(-3) =11`
`5+6=11`
`11=11`

It checks!

Our solution is correct.