Question 347549
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_<U>-21x+24y=123<u>_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