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Question 325875: How do I Solve the following using substitution method? I get lost when I try. Thanks
3x+y=5
x-2y=4
Answer by Apathious(24)   (Show Source):
You can put this solution on YOUR website! 3x+y=5_x-2y=4
Since 3x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 3x from both sides.
y=-3x+5_x-2y=4
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is -3x+5.
y=-3x+5_x-2(-3x+5)=4
Multiply -2 by each term inside the parentheses.
y=-3x+5_x+(6x-10)=4
Since x and 6x are like terms, add 6x to x to get 7x.
y=-3x+5_7x-10=4
Since -10 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 10 to both sides.
y=-3x+5_7x=10+4
Add 4 to 10 to get 14.
y=-3x+5_7x=14
Divide each term in the equation by 7.
y=-3x+5_(7x)/(7)=(14)/(7)
Simplify the left-hand side of the equation by canceling the common terms.
y=-3x+5_x=(14)/(7)
Simplify the right-hand side of the equation by simplifying each term.
y=-3x+5_x=2
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is 2.
y=-3(2)+5_x=2
Multiply -3 by each term inside the parentheses.
y=-6+5_x=2
Add 5 to -6 to get -1.
y=-1_x=2
This is the solution to the system of equations.
y=-1_x=2
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