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

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)   (Show Source): You can put this solution on YOUR website!
1.
2.
Subtract eq. 2 from eq. 1 to eliminate .

Then use either equation to solve for .

Answer by acalgebra(30)   (Show Source): You can put this solution on YOUR website!
First, multiply the second equation by -1:

Now, add the equations together:

Combine like terms:

Substitute y for 4 in one of the equations. I chose the first one:

Multiply 3 by 4:

Subtract 12 from both sides:

So, and .
--------
Check:
First equation:

Second equation:

Answer by CharlesG2(834)   (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

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