Question 81713: Solve the system by substitution.
x + 2y = 11
–2x + 4y = –6
Answer:
x =
y =
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
.
+ x + 2y = 11
–2x + 4y = –6
.
Solve the top equation for x. Do this by subtracting 2y from both sides to make the top
equation become:
.
x = 11 - 2y
.
Then go to the bottom equation and substitute 11 - 2y for x. When you do that substitution,
the bottom equation becomes:
.
-2(11 - 2y) + 4y = -6
.
Do the distributed multiplication on the left side by multiplying -2 times both of the
terms inside the parentheses. Doing that multiplication results in:
.
-22 + 4y + 4y = -6
.
Get rid of the -22 on the left side by adding 22 to both sides. This makes the equation:
.
+4y + 4y = 16
.
Add the two terms on the left side to get:
.
8y = 16
.
Solve for y by dividing both sides by 8, the multiplier of y. This division results
in:
.
y = 16/8 = 2
.
Now that we know that y is 2, we can return to one of the two original equations,
substitute 2 for y in that equation and solve for x. Let's return to the top equation:
.
x + 2y = 11
.
Substitute 2 for y and get:
.
x + 2(2) = 11
.
Multiply out:
.
x + 4 = 11
.
Get rid of the 4 on the left side by subtracting 4 from both sides to get:
.
x = 11 - 4 = 7
.
So the answers to this problem are x = 7 and y = 2.
.
Hope this helps you to understand the problem and how to work out a solution by substitution.
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