# Solve by Addition/Elimination x-y=2 , 3x+z=11 , y-2z=-3

, ,
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 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.
Simplify .
Apply the distributive property.
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 .
Divide by .
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.
Solve for .
Multiply by .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
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 .
Multiply by .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.