Question 268761: 5x + 3y = -10
3x + 5y= -6
how do you solve the system of equations by elimination
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! 5x+3y=-10_3x+5y=-6
=►Multiply each equation by the value that makes the coefficients of x equal. This value is found by dividing the least common multiple of the coefficients of x by the current coefficient. In this case, the least common multiple is 15.
3*(5x+3y=-10)_5*(3x+5y=-6)
=►Multiply each equation by the value that makes the coefficients of x equal. This value is found by dividing the least common multiple of the coefficients of x by the current coefficient. In this case, the least common multiple is 15.
3*(5x+3y)=3(-10)_5*(3x+5y)=5(-6)
=►Multiply 3 by each term inside the parentheses.
3*(5x+3y)=-30_5*(3x+5y)=5(-6)
=►Multiply 3 by each term inside the parentheses.
(15x+9y)=-30_5*(3x+5y)=5(-6)
=►Remove the parentheses around the expression 15x+9y.
15x+9y=-30_5*(3x+5y)=5(-6)
=►Multiply 5 by each term inside the parentheses.
15x+9y=-30_5*(3x+5y)=-30
=►Multiply 5 by each term inside the parentheses.
15x+9y=-30_(15x+25y)=-30
=►Remove the parentheses around the expression 15x+25y.
15x+9y=-30_15x+25y=-30
=►Multiply the first equation by -1 to make the coefficients of x have opposite signs.
-(15x+9y)=-(-30)_15x+25y=-30
=►Multiply -1 by the -30 inside the parentheses.
-(15x+9y)=30_15x+25y=-30
=►Multiply -1 by each term inside the parentheses.
(-15x-9y)=30_15x+25y=-30
=►Remove the parentheses around the expression -15x-9y.
-15x-9y=30_15x+25y=-30
=►Add the two equations together to eliminate x from the system.
15x+25y=-30_-15x-9y=30_ 16y= 0
=►Divide each term in the equation by 16.
y=0
=►Substitute the value found for y into the original equation to solve for x.
-15x-9(0)=30
=►Multiply -9 by each term inside the parentheses.
-15x+0=30
=►Remove the 0 from the polynomial; adding or subtracting 0 does not change the value of the expression.
-15x=30
=►Divide each term in the equation by -15.
x=-2
=►This is the final solution to the independent system of equations.
y=0_x=-2
|
|
|
