Question 55894: QUESTION: SOLVE THE SYTEM BY ADDITION
-5X+2Y=10
X-3Y=11
Answer by junior403(76)   (Show Source):
You can put this solution on YOUR website! SOLVE THE SYTEM BY ADDITION
-5X+2Y=10
X-3Y=11
First we can add these equations vertically.
-5X+2Y=10
....X-3Y=11
__________
-4X-1Y=21
Ok so far?
Now we can solve this result for one of the variables. Lets choose Y.
-4X-Y=21
We can add 4X to both sides to move it to the right.
-Y=21+4X
Then we can divide each side of the equation by -1 to make the Y positive.
Y=-21-4X
Now that we have the value for Y we can insert that value into one of our original equations.
X - 3(-21-4X) = 11
Ok?
Now we can solve for X.
first we can distribute the -3 with everything inside the parentesis.
X + 63 +12X = 11
Then we can subtract 63 from both sides.
X + 12X = -52
Then we combine like terms.
13X = -52
Then we can divide both sides by 13.
X = -4
Now that we know the value of X, we can substitute the -4 in the other original equation.
-5(-4)+2Y=10
Distribute.
20 + 2Y = 10
Subtract 20 from both sides.
2Y = -10
Divide by 2.
Y = -5
So X = -4 and Y = -5
To check this we can apply both results to one or both of the originals.
-5X+2Y=10
-5(-4)+2(-5)=10
20 -10 = 10 TRUE
X-3Y=11
(-4)-3(-5)=11
-4 + 15 = 11 TRUE
I hope this helps.
Good Luck!
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