Solve the system by back substitution calculator

Gaussian elimination method with back substitution

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Gaussian elimination

The calculator solves the systems of linear equations using the row reduction (Gaussian elimination) algorithm. The calculator produces step by step solution description.

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 PLANETCALC, Gaussian elimination method with back substitution

frederick bediako2020-05-06 07:38:23

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Consider a system with the given row-echelon form for its augmented matrix.

The equations for this system are

\(\eqalign{x - 2y + z &= 4\\y + 6z &= - 1\\z &= 2}\)

The last equation says z = 2. Substitute this into the second equation to get

\(\eqalign{y + 6\left( 2 \right) &= - 1\\y &= - 13}\)

Now substitute z = 2 and y = –13 into the first equation to get

\(\eqalign{x - 2\left( { - 13} \right) + \left( 2 \right) &= 4\\x &= - 24}\)

Thus the solution is x = –24,y = –13, and z = 2.

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Learn how to use the Algebra Calculator to solve systems of equations.

Example Problem

Solve the following system of equations:
x+y=7, x+2y=11

How to Solve the System of Equations in Algebra Calculator

First go to the Algebra Calculator main page.

Type the following:

1. The first equation x+y=7
2. Then a comma ,
3. Then the second equation x+2y=11

Try it now: x+y=7, x+2y=11

Clickable Demo

Try entering x+y=7, x+2y=11 into the text box.

After you enter the system of equations, Algebra Calculator will solve the system x+y=7, x+2y=11 to get x=3 and y=4.

More Examples

Here are more examples of how to solve systems of equations in Algebra Calculator. Feel free to try them now.

• Solve y=x+3, y=2x+1: y=x+3, y=2x+1
• Solve 2x+3y=5, x+y=4: 2x+3y=5, x+y=4

Need Help?

Please feel free to Ask MathPapa if you run into problems.

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