Question 1085729: Linear equation must be solved by elimination
2x-y=32
y-5x=13 Found 4 solutions by Fombitz, rothauserc, MathTherapy, Theo:Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website! Add the equations to eliminate y.
Solve for x then solve for y. Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website! 1) 2x - y = 32
2) y - 5x = 13
:
solve equation 2 for y
:
y = 5x + 13
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substitute for y in equation 1
:
2x - (5x + 13) = 32
:
2x - 5x - 13 = 32
:
-3x = 45
:
x = -15
:
y = 5(-15) + 13
:
y = -62
:
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x = -15 and y = -62
:
check answer by substituting for x and y in equations 1 and 2
:
1) 2(-15) - (-62) = 32
-30 + 62 = 32
32 = 32
:
2) -62 - 5(-15) = 13
-62 + 75 = 13
13 = 13
:
our answer checks
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Correct response is from:
IGNORE the one that used substitution. That person is not helping you!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! elimination means you manipulate the equations by multiplying or dividing one or both of the equations so that one of the variables will cancel out and you can then solve for the variable that remains.
the equations are:
2x - y = 32
y - 5x = 13
you would like to re-arrange the variables so like variables are underneath each other, and constants are underneath each other.
you will get:
2x - y = 32
-5x + y = 13
add the equations together and the y variables will cancel out and disappear.
when you add equations together, you add like variables to each other on both sides of the equal sign.
if like variables or constants are not on the same side of the equation, re-arrange the equation to make them so.
in this case, like variables and constants are already on the same side of the equation, so this step is not necessary.
the addition of like variables and constants goes like this:
2x - 5x = -3x
-y + y = 0
32 + 13 = 45
you will get -3x = 45
divide both sides of this equation by -3 to get x = -15.
that's the value of x you are looking for.
once you've solved for one of the variables, go back to the original equations and solve for the other variable using any one of the equations.
the original equations are:
2x - y = 32
y - 5x = 13
with 2x - y = 32, you get -30 - y = 32
add 30 to both sides of the equation to get -y = 62
multiply both sides of the equation by -1 to get y = -62
you have now solved for the value of both variables.
those are: x = -15 and y = -62
go back to your original equations and evaluate each one with them with the values you solved for to see if the equations hold true.
your original equations are, once again:
2x - y = 32
y - 5x = 13
after replacing x with -15 and y with -62, they become:
2 * (-15) - (-62) = 32
-62 - 5 * (-15) = 13
-30 + 62 = 32
-62 + 75 = 13
combine like terms to get:
32 = 32
13 = 13
the original equations are true which confirms the solution is correct.