SOLUTION: Find the solution to each system by the substitution method. Check your answers. 10x+3y=8 2x+y+2

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Question 773373: Find the solution to each system by the substitution method. Check your answers.
10x+3y=8
2x+y+2

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I believe you meant
system%2810x%2B3y=8%2C2x%2By=2%29

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%2810x%2B3y=8%2C2x%2By=2%29
Solving for y in 2x%2By=2 is the easiest way to start:
2x%2By=2 --> y=2-2x (subtracting 2x from both sides of the equal sign.
Next we substitute 2-2x for y in 10x%2B3y=8:
10x%2B3%282-2x%29=8-->10x%2B3%2A2-3%2A2x=8 (applying the distributive property)
10x%2B3%2A2-3%2A2x=8-->10x%2B6-6x=8 (doing the indicated operations)
10x%2B6-6x=8-->10x-6x=8-6-->10x-6x=2 (subtracting 6 from both sides)
10x-6x=2-->%2810-6%29x=2-->4x=2 (taking out x as a common factor, sometimes called "collecting like terms")
4x=2-->x=2%2F4-->highlight%28x=1%2F2%29 (dividing both sides by 4)
Now we substitute 1%2F2 for x in the solved-for-y equation y=2-2x above:
y=2-2%2A%281%2F2%29-->y=2-1-->highlight%28y=1%29

Checking the answer highlight%28system%28x=1%2F2%2Cy=1%29%29:
10x%2B3y=10%2A%281%2F2%29%2B3%2A1=5%2B3=8 verifies 10x%2B3y=8
2x%2By=2%2A%281%2F2%29%2B1=1%2B1=2 verifies 2x%2By=2