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

Aug 5, 2015

There is an infinite number of solutions.

#### Explanation:

One way is to use the method of substitution.

Step 1. Enter the equations.

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

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

[2] $y = 3 x + 2$

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 $x$.

$6 x - 2 \left(3 x + 2\right) = - 4$

$6 x - 6 x - 4 = - 4$

$- 4 = - 4$

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 $y$.

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

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