Question

How do you solve `6x-2y=-4` and `y=3x+2`?

Answer 1

There is an infinite number of solutions.

Explanation:

One way is to use the method of substitution.

Step 1. Enter the equations.

[1] `6x-2y=-4`
[2] `y=3x+2`

Step 2. Solve for one variable in terms of the other.

[2] `y=3x+2`

Since this is already done for us, we can go on to the next step.

Step 3. Substitute Equation 2 in Equation 1 and solve for `x`.

`6x-2(3x+2) =-4`

`6x-6x-4 = -4`

`-4=-4`

This indicates that the solution consists of all real numbers and the equations are identical.

We can see that the equations are identical if we solve Equation 1 for `y`.

`2y=6x+4`
`y=3x+2`

Some answers that fit are (`-1,-1`), (`0,2`), and (`1,5`).