A system of equations is two (or more) equations in which the solution in which the same set of values for the variables satisfies all of the equations.

As a simple example, the two equations could be x + y =2 and x - y = 0. The solution for the system of equations is x = 1 and y =1.

Now an example of how to work the problem (feel free to use my steps, but change the numbers so that you do your own work).

I am going to pick to two integers between -12 and 12. In case, I will use 3 and -1.

I am now going to make up two problems that involve multiplying 3 by something and adding it to -1 multiplied by something and solve them

4 X **3** +2 X **(-1)** 2 X **3** - 1 X
**(-1)**

12 -2 6 + 1

10 7

Using these answers, I rewrite the problems, substituting x for 3, y for -1, and set them equat to the answers.

4x + 2y = 10 2x - y = 7

The system of equations is **1.** 4x + 2y = 10 and **2.** 2x - y = 7 (the bold numbers are for identifying the equations later. They are not part of the equation)

There are three methods of solving this equation: Graphing, Elimanation, and Substitution. Your question requires the elimination method (called addition/subtraction).

To solve a system of equations using elimination method, you will need to add or subtract a multiple of one equation from a multiple of the other so that one of the variables will be multiplied by zero (and be eliminated).

In my example, the sign on the y terms is opposite and the coefficient on **
1.** is twice the size of the coefficient on **2.** If I multiply **1.** by one (leave it the same) and multiply **2.** by two, I can add them together and get a coefficient of 0 on the y term. (See below)

1 X **1. **4x + 2y = 10 = 4x + 2y = 10

2 X **2. **2(2x - y) = (2)7 = 4x - 2y = 14

8x + 0y = 24

The result of adding the two equations is 8x + 0y = 24. Now we solve the equation to find x.

8x + 0y = 24

8x + 0 =24

8x = 24

x = 3

Once one of the terms (the value of x or y) is found, you just need to substitute it into one of the equations to find the other term. For example, we can substitue 3 for x in
**1.** to get 4 X 3 + 2y = 10.

4 X 3 + 2y = 10

12 + 2y = 10

2y = -2

y = -1

## Comments

You need to find a system of 2 equations and 2 variables (x and y).

can anyone show me an example?