SOLUTION: 5x-3y=-13 7x-8y=-41 solve by elimintion

Question 347549: 5x-3y=-13
7x-8y=-41 solve by elimintion
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
7x-8y=-41_5x-3y=-13
Multiply each equation by the value that makes the coefficients of y equal. This value is found by dividing the least common multiple of the coefficients of y by the current coefficient. In this case, the least common multiple is 24.
3*(7x-8y=-41)_8*(5x-3y=-13)
Multiply each equation by the value that makes the coefficients of y equal. This value is found by dividing the least common multiple of the coefficients of y by the current coefficient. In this case, the least common multiple is 24.
3*(7x-8y)=3(-41)_8*(5x-3y)=8(-13)
Multiply 3 by each term inside the parentheses.
3*(7x-8y)=-123_8*(5x-3y)=8(-13)
Multiply 3 by each term inside the parentheses.
21x-24y=-123_8*(5x-3y)=8(-13)
Multiply 8 by each term inside the parentheses.
21x-24y=-123_8*(5x-3y)=-104
Multiply 8 by each term inside the parentheses.
21x-24y=-123_40x-24y=-104
Multiply the first equation by -1 to make the coefficients of y have opposite signs.
-(21x-24y)=-(-123)_40x-24y=-104
Multiply -1 by each term inside the parentheses.
-(21x-24y)=123_40x-24y=-104
Multiply -1 by each term inside the parentheses.
-21x+24y=123_40x-24y=-104
Add the two equations together to eliminate y from the system.
40x-24y=-104_-21x+24y=123_19x = 19
Divide each term in the equation by 19.
x=1
Substitute the value found for x into the original equation to solve for y.
-21(1)+24y=123
Multiply -21 by each term inside the parentheses.
-21+24y=123
Move all terms not containing y to the right-hand side of the equation.
24y=144
Divide each term in the equation by 24.
y=6
This is the final solution to the independent system of equations.
x=1_y=6
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