SOLUTION: 2x + 5y = 2 2x - 2y = -12 I am completely stuck on how to go about doing this problem. I think that the Solutions x and y are always intergers between 5 and -5. I dont underst

Question 149217: 2x + 5y = 2
2x - 2y = -12
I am completely stuck on how to go about doing this problem.
I think that the Solutions x and y are always intergers between 5 and -5.
I dont understand how to do the substitution.. im used to X or Y being alone with no other number.
x = ?
Y = ?
If you could, please show me a few steps on How to get the answer
to this problem.
I would greatly appreciate your help
Thank You,
Kerry G
Found 2 solutions by nerdybill, Earlsdon:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
2x + 5y = 2 (equation 1)
2x - 2y = -12 (equation 2)
.
This site describes the "substitution method" quite well:
http://www.purplemath.com/modules/systlin4.htm
.
Solve equation 2 for x:
2x - 2y = -12
2x = 2y -12
x = y - 6
.
Using the above definition of x, we plug it in to equation 1 and solve for y:
2x + 5y = 2
2(y - 6) + 5y = 2
2y - 12 + 5y = 2
7y - 12 = 2
7y = 14
y = 2
.
Plug the above back into equation 2 and solve for x:
2x - 2y = -12
2x - 2(2) = -12
2x - 4 = -12
2x = -8
x = -4
.
Solution:
x = -4
y = 2

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
G'day Kerry G., what you have here is a system of equations, in this case, two equations with two unknowns (x and y).
There several methods for solving systems of equations, but the basic idea is to first eliminate one of the variables and solve for the other. Then you substitute the solved variable into either one of the two equations to solve for the other variable...and it's not as formidable as sounds!
Starting with the two given equations:
1) and
2) It looks like you can eliminate the x variable by subtracting one equation from the other. Let's subtract equation 2) from equation 1). (It doesn't much matter which equation you subtract from which, it will work anyway)

-()
----------------------
You can see that the x variable has been eliminated. Now solve for y by dividing both sides of this equation by 7.
Now that you have the value of y, you substitute this into either one of the two given equations to solve for x. Let's use equation 1).
Substitute y = 2.

Subtract 10 from both sides.
Finally, divide both sides by 2.

So the solution is (-4, 2)
What this means is that if you were to graph the given two linear equations, you would see two lines that intersect, and the point at which they intersect is the "solution" to the system of equations.
Of course, graphing the two equations is another method of solving.
Let's look at the graph:

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