When you add the equations together, you get an equation in x. (You have eliminated y.) When you subtract one equation from the other, you get an equation in y. (You have eliminated x.)
Adding the equations:
(3x-4y) + (3x+4y) = (24) + (24)
6x = 48 (collect terms. The y terms cancel--add to zero.)
x = 8 (divide both sides of the equation by 6)
Subtracting the equations:
(3x-4y) - (3x+4y) = (24) - (24)
-8y = 0 (collect terms. The x terms cancel, that is, they add to zero.)
y = 0 (divide both sides of the equation by -8)
The solution is (x, y) = (8, 0).
When you solve by elimination, you want to choose some multiple of one equation that will cause one of the variables to be eliminated when added to some multiple of the other equation. Because the x coefficients are the same in your equations, we can eliminate x by subtracting one equation from the other. Because the y coefficients are opposites, we can eliminate y by adding one equation to the other.
If the coefficient have some other relationship, we might have to multiply one or both equations by some number(s) before doing the addition or subtraction.
Adding the equations:
(3x-4y) + (3x+4y) = (24) + (24)
6x = 48 (collect terms. The y terms cancel--add to zero.)
x = 8 (divide both sides of the equation by 6)
Subtracting the equations:
(3x-4y) - (3x+4y) = (24) - (24)
-8y = 0 (collect terms. The x terms cancel, that is, they add to zero.)
y = 0 (divide both sides of the equation by -8)
The solution is (x, y) = (8, 0).
When you solve by elimination, you want to choose some multiple of one equation that will cause one of the variables to be eliminated when added to some multiple of the other equation. Because the x coefficients are the same in your equations, we can eliminate x by subtracting one equation from the other. Because the y coefficients are opposites, we can eliminate y by adding one equation to the other.
If the coefficient have some other relationship, we might have to multiply one or both equations by some number(s) before doing the addition or subtraction.
