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

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Answer 1 · 2015-08-05T21:18:32

There is an infinite number of solutions.

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 ( $1,5$ ).

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