Question 1190990: Solve this system of linear equations using substitution: x - 7y = -11; and 5x + 2y = -18 Found 2 solutions by math_tutor2020, ikleyn:Answer by math_tutor2020(3817) (Show Source):
We'll then plug this into the other equation.
Wherever you see an x, replace it with (-11+7y)
The term "substitute" effectively means "replace".
So,
5x + 2y = -18
5(-11+7y) + 2y = -18
-55+35y + 2y = -18
-55+37y = -18
37y = -18+55
37y = 37
y = 37/37
y = 1
We can now find x based on that
x = -11+7y
x = -11+7(1)
x = -11+7
x = -4
Solution: x = -4 and y = 1
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Check:
Plug x = -4 and y = 1 into the first original equation
x-7y = -11
-4-7(1) = -11
-4-7 = -11
-11 = -11
Repeat for the other original equation as well
5x + 2y = -18
5(-4) + 2(1) = -18
-20 + 2 = -18
-18 = -18
For each equation above, we get a true statement (i.e. the same number on both sides).
The solution is fully confirmed.
You can put this solution on YOUR website! .
Solve this system of linear equations using substitution:
x - 7y = -11
5x + 2y = -18
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x - 7y = -11 (1)
5x + 2y = -18 (2)
From equation (1), express x = 7y - 11 and substitute it into equation (2). You will get
5*(7y - 11) + 2y = -18.
Thus you have an equation for one single unknown y. Simplify it and find y
35y - 55 + 2y = -18
35y + 2y = 55 - 18
37y = 37.
y = = 1.
Now substitute this value of y into equation (1) to get
x - 7*1 = -11,
x = -11 + 7 = -4.
Answer. The solution is x= -4; y= 1.
Check the solution on your own by substituting the found values into the original equations.
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