
Tamara J. answered 11/26/12
Math Tutoring - Algebra and Calculus (all levels)
-13x + 8y = -6
3x - 4y = 2
To solve for a system of linear equations by the method of elimination, we need to manipulate one or both equations in the system in a way that will eliminate one of the variables so as to solve for the remaining variable. Once we have solved for one of these variables, we use it to solve for the other variable by plugging it back into one of the original equations.
For the system of linear equations above, the simplest way to eliminate one of the variables seems to be by multiplying the second equation by 2, which will yield a -8y thus eliminating the y variable and solving for x.
3x - 4y = 2 multiply the entire equation by 2
2*(3x - 4y = 2) ==> 2*(3x) - 2*(4y) = 2*(2) ==> 6x - 8y = 4
Now we add the first equation to the new second equation:
-13x + 8y = -6
+ 6x - 8y = 4
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-13x + 6x + 8y - 8y = -6 + 4
-7x + 0 = -2
-7x = -2
x = 2/7
Plug in the answer for x into one of the original equations above to solve for y:
-13x + 8y = -6
plug in 2/7 for x
-13(2/7) + 8y = -6 ==> -26/7 + 8y = -6
add 26/7 to both sides of the equation
-26/7 + 8y + 26/7 = -6 + 26/7 ==> 0 + 8y = -6 + 26/7
multiply -6 by 7/7 to yield a least common denominator
8y = -6(7/7) + 26/7 ==> 8y = -42/7 + 26/7 = (-42+26)/7
8y = -16/7
divide both sides of the equation by 8 to solve for y
(8y) / 8 = (-16/7) / 8 ==> 1y = (-16/7) / (8/1)
when dividing fractions, multiply the numerator by the reciprocal of the denominator
y = (-16/7)*(1/8) = (-16*1) / (7*8)
y = -16/56
simplify the fraction
y = -2/7
Thus, the solution to this system of linear equations is: x = 2/7 , y = -2/7
OR (2/7 , -2/7)