# Solve by Addition/Elimination 4a+7b=-51 , 8a+3b=-20 , 6b+3c=18

, ,
Choose two equations and eliminate one variable. In this case, eliminate .
Eliminate from the system.
Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
Simplify .
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Multiply by .
Add the two equations together to eliminate from the system.
The resultant equation has eliminated.
Take the resultant equation and the third original equation and eliminate another variable. In this case, eliminate .
Eliminate from the system.
Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
Multiply by .
Multiply by .
Simplify .
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Multiply by .
Add the two equations together to eliminate from the system.
The resultant equation has eliminated.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Substitute the value of into an equation with eliminated already and solve for the remaining variable.
Substitute the value of into an equation with eliminated already.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
Substitute the value of each known variable into one of the initial equations and solve for the last variable.
Substitute the value of each known variable into one of the initial equations.
Solve for .
Simplify each term.
Multiply .
Multiply by .
Combine and .
Multiply by .
Move the negative in front of the fraction.
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
This is the final solution to the system of equations.
Solve by Addition/Elimination 4a+7b=-51 , 8a+3b=-20 , 6b+3c=18