SOLUTION: Addition method x+y=7 x-y=9 x-2y=-1 -x+5y=4 3x + 5y = -11 x- 2y = 11 2x= 2-y 3x + y =-1

Question 204179: Addition method
x+y=7
x-y=9

x-2y=-1
-x+5y=4

3x + 5y = -11
x- 2y = 11

2x= 2-y
3x + y =-1

Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
I'll give you a couple of examples that should clear things up and then how about if you try on your own. Then if it doesn't work out... come back and ask again, k?

So your first system:

x+y=7
x-y=9

If you were to add those together, do you see a variable that would immediately drop out?

How about this:
x+y=7
x-y=9
_______
2x =16 (see how +y - y = 0)
x = 8 (divided both sides by 2 to isolate the x)

Now that you know what "x" is, then fill that info into one of the original equations. I'll choose the first one:
X + y = 7 (x=8 so fill that in)
8 + y = 7 (now subtract both sides by 8 to isolate the y)
y = -1

Does this work? Let's fill out the equations with our values for x and y....

x+y=7 (original equation)
8 - 1 = 7 (see how the values for x and y are plugged in here?)
7 = 7. THIS WORKS!

x-y=9 (2nd original equation)
8 - (-1) = 9 (plugged in values)
8 + 1 = 9
9 = 9 THIS works, too! Yayyyyy. :-)

So ok, that works easily when you can see easily what variable is quickly lost in adding the two equations.

In this system, tho, the "lost" variable is not apparent....

3x + 5y = -11
x- 2y = 11 (SO.. how about if we multiply this WHOLE equation by -3?)

Then we'd have
3x + 5y = -11
-3x + 6y = -33 (see how the multiplication of -3 changed everything in the 2nd equation?)

Now add

3x + 5y = -11
-3x + 6y = -33
_______________
11y = -44
y = -4 (divided both sides by 11 to isolate the y)

Now we know y = -4. Let's plug that into one of the original equations......

x- 2y = 11 (original equation)
x -2(-4) = 11 (plugged in value for y)
x + 8 = 11 (multiplied -2 times -4)
x = 3 (subtracted 8 from both sides to isolate the x)

Now we know x = 3 and y = -4. Does this work? Let's look at our original equations........

3x + 5y = -11 (original equation)
3(3) + 5(-4) = -11 (plugged in info for x and y)
9 - 20 = -11
-11 = -11 This works! :-)

x- 2y = 11 (2nd equation)
3 - 2(-4) = 11 (plugged in info for x and y)
3 + 8 = 11
11 = 11 This works too! :-)

See if you can solve the other questions on your own, now that you have seen these two examples, k? I hope this helped you. :-)
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