Solving a Linear System in Three Variables with a Solution - Concept

Concept Concept (1)

In Algebra II, sometimes we will be asked to solve systems of equations three variables. When solving these systems of equations, a 3D coordinate system is necessary since systems of equations with three variables are not linear. Therefore, solving these systems of equations by graphing is not possible. Solving by substitution would be difficult, so we often solve by addition and elimination.

Sample Sample Problems (4)

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Solving a Linear System in Three Variables with a Solution - Problem 1

Solve the system:

2x + y − z = 5
x + 4y + 2x = 16
15x + 6y − 2x = 12
Problem 1
How to solve a system of linear equations in three variables.
Solving a Linear System in Three Variables with a Solution - Problem 2

Solve the system:

4a + 2b − 3c = 6
a − 4b + c = -4
-a + 2c = 2
Problem 2
How to solve a system of linear equations in three variables.
Solving a Linear System in Three Variables with a Solution - Problem 3
Problem 3
Using substitution to solve a 3 x 3 system of equations.
Solving a Linear System in Three Variables with a Solution - Problem 4
Problem 4
Solving a 3 x 3 system of equations using elimination.