Systems of Equations and Inequalities: Systems of Equations with Three Variables

section warm up Section Warm-Up

Before we begin working with solving systems of equations with three variables, let’s review some of the skills you learned when working with matrices.

think icon Think & Click: Review of Matrices

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

Find the inverse of A.

A equals a  two by two matrix with row one: 2, negative 4, and row two:  negative 2, 5

A inverse equals a two by two matrix with row one: five-halves, 2, and row two: 1, 1
 

Multiply AB

A equals a two by two matrix with row one: 5, negative 1, and row two: 2, 6

A equals a two by one matrix with row one a 3 and row two a negative 2

A times B equals a two by one matrix with row one a 17 and row two a negative 6
 

Solve this system using matrices:

2x + 5y = 13
x + 3y = 8

the two by two matrix with row one: 2, 5 and row two: 1, 3, times the two by one matrix with row one an x and row two a y, equals the two by one matrix with row one a 13 and row two an 8

x equals negative 1 and y equals 3