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Question 68775: Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-4x + y = 8
2x + 3y = -1
Answer by rmromero(383)   (Show Source):
You can put this solution on YOUR website!
Here are the Steps using Substition method
1. In either equation, solve for one variable in terms of the other.
-4x + y = 8
y = 4x + 8
2. Substitute 4x + 8 for y in the other equation. Solve x.
2x + 3y = -1
2x + 3(4x + 8) = -1
2x + 12x + 24 = -1
14x + 24 = -1
14x = -25
x = -25/14
3. Substitute the result from step 2 in either equation 2x + 3y = -1.
Solve for the other variable.
-4x + y = 8 , x = -25/14
-4(-25/14) + y = 8
100/14 + y = 8
y = 12/14
4. Check the solution in both original equations.
2x + 3y = -1, x = -25/14, y = 12/14
2(-25/14) + 3(12/14) = -1
-50/14 + 36/14 = -1
-14/14 = -1
-1 = -1 ----------->True
-4x + y = 8, x = -25/14, y = 12/14
-4(-25/14) + (12/14) = 8
100/14 + 12/14 = 8
112/14 = 8
8 = 8 ----------->>True
There is a unique solution, (-25/14, 12/14)
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