Question

Write and solve a system of equations. Be sure to label the variables. The sum of two numbers is twelve. Two times the first number minus three times the second number is four. What are the two numbers? Show and Explain all work.

Answer 1

The solution to the system of equations is x = 8, y = 4.

How to write the system of equations?

First, let's define our variables as x and y.

"the sum of two numbers is twelve" is written as:

x + y = 12

"two times the first number minus three times the second number is four" is written as:

2x - 3y = 4

Then the system of equations is:

x + y  = 12

2x - 3y = 4

How to solve it?

First, we isolate one of the variables in one equation, I will isolate x on the first one to get:

x = 12 - y

Now we replace this on the other equation, so we get:

2*(12 - y) - 3y = 4

Now we can solve this for y.

24 - 2y - 3y = 4

24 - 5y = 4

24 - 4 = 5y

20/5 = y = 4

Now we know the value of y, and:

x = 12 - y = 12 - 4 = 8

Then the solution of the system is:

x = 8, y = 4.

If you want to learn more about systems of equations, you can read:

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