IXL - Solve a system of equations using augmented matrices (Algebra 1 practice)

Solve using augmented matrices.

^–3x − 6y = ^–6

y = ^–3

(, )

ref_doc_title.

Learn with an example

question

Solve using augmented matrices.

^–3x − 7y = ^–1

x = ^–2

(, )

key idea

To solve using augmented matrices, follow these three steps:

Step 1: Write the augmented matrix.

Step 2: Use elementary row operations to transform the left part of the augmented matrix into the identity matrix.

Step 3: State the solution.

solution

Use augmented matrices to solve the system of equations:

^–3x − 7y = ^–1

x = ^–2

Step 1: Write the augmented matrix.

Since both equations are in standard form, you can write the numbers in an augmented matrix.

^–3x + ^–7y = ^–1

1x + 0y = ^–2

→

^–3	^–7		^–1
1	0		^–2

Step 2: Use elementary row operations to transform the left part of the augmented matrix into the identity matrix.

There are three elementary row operations:

Swap any two rows

Multiply any row by a non-zero number

Add a multiple of any row to any other row

Use these three operations to make the part of the matrix to the left of the dashed line look like the identity matrix:

1	0
0	1

Start with the augmented matrix from Step 1.

^–3	^–7		^–1
1	0		^–2

1	0		^–2
^–3	^–7		^–1

Swap R₁ with R₂

1	0		^–2
0	^–7		^–7

Add 3R₁ to R₂

1	0		^–2
0	1		1

Multiply R₂ by

^–1

The left part is now the identity matrix, so no more row operations need to be performed.

Step 3: State the solution.

The solution is the last column of the new matrix.

1	0		^–2
0	1		1

The solution is (^–2, 1).

Looking for more? Try this:

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

LL.1Matrix vocabulary

O.1Is (x, y) a solution to the system of equations?

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!