, ,

Choose two equations and eliminate one variable. In this case, eliminate .

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 .

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.

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.

Solve for .

Multiply by .

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Add and .

The solution to the system of equations can be represented as a point.

The result can be shown in multiple forms.

Point Form:

Equation Form:

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