SOLUTION: Find the solution to each system by the substitution method. Check your answers. 3x-5y= -7 x-4y=-7

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Question 773372: Find the solution to each system by the substitution method. Check your answers.
3x-5y= -7
x-4y=-7

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
When solving a system by substitution, you start by solving for one of the variables in one of the equations.
It is easier if you look for a variable with a coefficient of 1 or -1, meaning that you look for a variable that does not have a number in front, at most it has a + or - sign.
For example,
in 2x-y=2, it is easiest to solve for y,
while in x%2B4y=5, it is easiest to solve for x.
Solving for the variable gives you an expression for that variable as a function of the other variable(s).
Then you substitute that expression into the other equation(s).

system%283x-5y=+-7%2Cx-4y=-7%29
Solving for x in x-4y=-7 is easiest:
x-4y=-7 --> x=4y-7 (adding 4y to both sides of the equal sign.
Next we substitute 4y-7 for x in 3x-5y=+-7:
3%284y-7%29-5y=+-7-->3%2A4y-3%2A7-5y=+-7 (applying the distributive property)
3%2A4y-3%2A7-5y=+-7-->12y-21-5y=+-7 (doing the indicated operations)
12y-21-5y=+-7-->12y-5y=+-7%2B21-->12y-5y=14 (adding 21 to both sides)
12y-5y=14-->%2812-5%29y=14-->7y=14 (taking out y as a common factor, sometimes called "collecting like terms")
7y=14-->y=14%2F7-->highlight%28y=2%29 (dividing both sides by 7)
Now we substitute 2 for y in the solved-for-x equation x=4y-7 above:
x=4%2A2-7-->x=8-7-->highlight%28x=1%29

Checking the answer highlight%28system%28x=1%2Cy=2%29%29:
3x-5y=3%2A1-5%2A2=3-10=-7 verifies 3x-5y=-7
x-4y=1-4%2A2=1-8=-7 verifies x-4y=-7