Lesson 1.5: Using Systems of Equations

Advanced Math Topics

Mrs. Mongold

How do you solve a system using matrices?

• System of Equations: Consists of two or more equation involving the same variables

• Example:x + y = 10,000

7x + 9y = 85,000

How do you solve a system using matrices?

• Augmented Matrix: a matrix form of a linear system of equations obtained from the coefficient matrix and constants

• ExamplesMatrix Equation Augmented Matrix

How do you solve a system using matrices?

• Reduced Row Echelon Form (rref): each row contains only 0’s until the first nonzero element, which must be a 1

• Each row has the 1 further to the right than the previous row

• All entries above and below the 1st 1 in each row must be 0’s

• Examples:

How do you solve a system using matrices?

• Something to rememberSystem of Equations in two variables

ax + by = c

dx + ey = f

Matrix Equation

Solution

f

c

y

x

ed

ba

BAy

x 1

Let’s use the calculators

• Using our system from the first slidex + y = 10,000

7x + 9y = 85,000

Additional Examples

402

50

xy

yx

xy

yx

06.08.202.

3046812

23

1

24

3

yx

yx

25.25.1

1233.225.1

yx

xy

Homework

• Pg 34/ 3-11 odd