SOLUTION: solve by elimination x+6y=41 -x-2y=7

Question 172876: solve by elimination
x+6y=41
-x-2y=7
Found 2 solutions by Mathtut, colliefan:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
solving by elimination is simply adding or subtracting one equation from another
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with the intention of eliminating one of the variables.
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so lets line the equations up one under the other to have a better look at each variable.
:
x+6y=41....eq 1
-x-2y=7.....eq 2
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It just so happens this set of equations needs no manipulation. As you observe the equations you will notice that the x terms are all set up for elimination when you add the two equations together because x-x=0.........we are left with the y terms and the constants... 6y-2y=41+7
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4y=48
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.
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now we take y's value and plug it back into either original equation to solve for x I choose eq 1
:
x+6(12)=41
:
x+72=41
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Answer by colliefan(242) (Show Source): You can put this solution on YOUR website!
solve by elimination
x+6y=41
-x-2y=7

Elimination means elimination of one variable so that you can solve for the remaining variable. To do this, add the 2 equation together. In this case, this will work well because one equation has x and the other has -x, so if you add them together x - x will equal zero and the resulting equation will only have Y and can be solved for Y.

x + 6y = 41
+ -x - 2y = 7
__________________
0x + 4y = 48

4y = 48
y = 12

Now substitute 12 into one of the equations to solve for x.
Using the first equation:
x+6y=41
x+ 6(12)=41
x=41-72
x = -31

Plug the values of x = -31 and y = 12 into both of the equations to check your results and make sure that these are a solution to both equations.
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