Solving 3-Variable Systems

What is the elimination method used for in solving 3-variable systems?

• To substitute variables in a system of equations

• To graphically represent a system of equations

• To find the determinant of a matrix

• To eliminate variables in a system of equations

When using the elimination method, what is the first step to eliminate one variable?

• Multiply one or both equations by a constant

• Subtract one equation from the other

• Divide one equation by a constant

• Add one equation to the other

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following system of equations using the elimination method: 2x + 3y - z = 5 3x - 2y + 4z = 7 4x + y + 2z = 3

What is the substitution method used for in solving 3-variable systems?

• To solve for one variable and substitute it into the other equations.

• To graph the system of equations.

• To solve for all variables simultaneously.

• To find the determinant of the coefficient matrix.

When using the substitution method, what is the first step to substitute one variable?

• Multiply both sides of the equation by a constant.

• Solve one of the equations for one variable in terms of the other variable.

• Simplify the equation.

• Rearrange the equation to isolate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following system of equations using the substitution method: x + 2y - z = 4 2x - y + 3z = 7 3x + y + 2z = 1

• The system of equations has infinitely many solutions.

• The system of equations has exactly one solution.

• The system of equations is dependent and has no unique solution.

• The system of equations is inconsistent and has no solution.

Which method is most suitable for solving 3-variable systems when the coefficients are simple and easy to work with?

• matrix method

• graphing method

• substitution method

• elimination method