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
12 -2 6 + 1
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