SOLUTION: I am supposed to solve a linear equation using the method of elimination, I have retried doing it over and over but when I go back to check my work it doesn't come out as the corre

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Question 369608: I am supposed to solve a linear equation using the method of elimination, I have retried doing it over and over but when I go back to check my work it doesn't come out as the correct answer. So I need help solving this by using method of elimination. Please help me solve this equation: x+3y=14
x+2y=10
Hopefully you know this method, I do but this particular problem is causing me to struggle, so can you show me the steps to how you figured it out? Thank you!
Found 3 solutions by Fombitz, acalgebra, CharlesG2:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x%2B3y=14
2.x%2B2y=10
Subtract eq. 2 from eq. 1 to eliminate x.
x%2B3y-x-2y=14-10
highlight%28y=4%29
Then use either equation to solve for x.
x%2B12=14
highlight%28x=2%29

Answer by acalgebra(30) About Me  (Show Source):
You can put this solution on YOUR website!
First, multiply the second equation by -1:
-x-2y=-10
Now, add the equations together:
x%2B3y-x-2y=14-10
Combine like terms:
x-x%2B3y-2y=4
y=4

Substitute y for 4 in one of the equations. I chose the first one:
x%2B3%284%29=14
Multiply 3 by 4:
x%2B12=14
Subtract 12 from both sides:
x=2

So, x=2 and y=4.
--------
Check:
First equation:
2%2B3%284%29=14
2%2B12=14
14=14
Second equation:
2%2B2%284%29=10
2%2B8=10
10=10

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
"I am supposed to solve a linear equation using the method of elimination, I have retried doing it over and over but when I go back to check my work it doesn't come out as the correct answer. So I need help solving this by using method of elimination. Please help me solve this equation: x+3y=14
x+2y=10
Hopefully you know this method, I do but this particular problem is causing me to struggle, so can you show me the steps to how you figured it out? Thank you!"

system of equations:
x + 3y = 14
x + 2y = 10

here is one way to do it:
choose a variable to eliminate,
change one of the equations by multiplying it against a value such that when the equations are added one of the variables cancels out eliminating that variable

multiply the 2nd equation by -1: -x - 2y = -10
add it to the 1st equation:
x - x + 3y - 2y = 14 - 10
y = 4
substitute y = 4 into x + 3y = 14
x + 3(4) = 14
x + 12 = 14
x = 2

check:
x + 3y = 14 --> 2 + 12 = 14, yes
x + 2y = 10 --> 2 + 8 = 10, yes