9.2 Systems of Equations in Three Variables

  • Solve systems of linear equations in three variables.

  • Use systems of three equations to solve applied problems.

  • Model a situation using a quadratic function.

A linear equation in three variables is an equation equivalent to one of the form Ax+By+Cz=D, where A, B, C, and D are real numbers and none of A, B, and C is 0. A solution of a system of three equations in three variables is an ordered triple that makes all three equations true. For example, the triple (2, -1, 0) is a solution of the system of equations


We can verify this by substituting 2 for x, 1 for y, and 0 for z in each equation.

Solving Systems of Equations in Three Variables

We will solve systems ...

Get Algebra and Trigonometry, 5th Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.