Question 343232: solve the following system using elimination: 2x-3y=7, 2y+x=-11
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 2x-3y=7,2y+x=-11
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 6.
2*(2x-3y=7)_3*(x+2y=-11)
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 6.
2*(2x-3y)=2(7)_3*(x+2y)=3(-11)
Multiply 2 by each term inside the parentheses.
2*(2x-3y)=14_3*(x+2y)=3(-11)
Multiply 2 by each term inside the parentheses.
4x-6y=14_3*(x+2y)=3(-11)
Multiply 3 by each term inside the parentheses.
4x-6y=14_3*(x+2y)=-33
Multiply 3 by each term inside the parentheses.
4x-6y=14_3x+6y=-33
Add the two equations together to eliminate y from the system.
3x+6y=-33_4x-6y=14_7x =-19
Divide each term in the equation by 7.
x=-(19)/(7)
Substitute the value found for x into the original equation to solve for y.
4(-(19)/(7))-6y=14
Multiply 4 by each term inside the parentheses.
-(76)/(7)-6y=14
Move all terms not containing y to the right-hand side of the equation.
-6y=(174)/(7)
Divide each term in the equation by -6.
y=-(29)/(7)
This is the final solution to the independent system of equations.
x=-(19)/(7)_y=-(29)/(7)
|
|
|
