how many solutions 2x+3y=−6 3x−4y=−12

Here is your system of equations:

When solving a system, you can either substitute or eliminate. I am going to eliminate because you can only substitute when there are answer choices.

When eliminating, you need either x or y to be the same or opposite(sign). I am going to eliminate y, whuch means 3y and -4y has to have the same number. To make them the same, I will multiply the two numbers because multiplying two numbers is an easier way to find a common multiple.

That means they both have to be changed so that their value is 12.

You have to multiply the first equation by 4.

For the second equation, I will have to multiply by 3 because:

Multiply the second equation by 3:

Here is your new system of equations:

Add:

y is eliminated because when a number is added/subtracted by its opposite, it's cancelled out.

Although the case is different, remember:

NEGATIVES

POSITIVES

Now you need to divide both sides by 17 to leave x alone.

Since x has a value, that means y also does. That also means the answer to your question is one solution.

this answer is !