Solving systems of linear equations by substitution

Q: What is solving a system by substitution?

The method of solving by substitution works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, substituting for the chosen variable and solving for the other.

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

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Example Problem
How to Solve the System of Equations in Algebra Calculator
Clickable Demo
More Examples
Related Articles
Number Line
How do you solve by substitution step by step?
How do you solve linear equations with two variables by substitution?
What is solving a system by substitution?
How do you solve a system of equations by substitution and elimination?

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:

The first equation x+y=7
Then a comma ,
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.

Algebra Calculator Tutorial

To solve systems using substitution, follow this procedure:

Select one equation and solve it for one of its variables.
In the other equation, substitute for the variable just solved.
Solve the new equation.
Substitute the value found into any equation involving both variables and solve for the other variable.
Check the solution in both original equations.

Usually, when using the substitution method, one equation and one of the variables leads to a quick solution more readily than the other. That's illustrated by the selection of x and the second equation in the following example.

Example 1

Solve this system of equations by using substitution.

Solve for x in the second equation.

Substitute

for x in the other equation.

Solve this new equation.

Substitute the value found for y into any equation involving both variables.

Check the solution in both original equations.

The solution is x = 1, y = –2.

If the substitution method produces a sentence that is always true, such as 0 = 0, then the system is dependent, and either original equation is a solution. If the substitution method produces a sentence that is always false, such as 0 = 5, then the system is inconsistent, and there is no solution.

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Examples

substitution\:x+y+z=25,\:5x+3y+2z=0,\:y-z=6
substitution\:x+2y=2x-5,\:x-y=3
substitution\:5x+3y=7,\:3x-5y=-23
substitution\:x+z=1,\:x+2z=4

substitution-system-of-equations-calculator

How do you solve by substitution step by step?

Steps to Solving by Substitution:.

Step One→ Solve one equation for either x or y..

Step Two→ Substitute the expression from step one into the 2nd equation..

Step Three→ Solve the second equation for the given variable..

Step Four→ Plug you solution back into the first equation..

Step Five→ Write your solution as a point..

How do you solve linear equations with two variables by substitution?

Linear Equations: Solutions Using Substitution with Two Variables.

Select one equation and solve it for one of its variables..

In the other equation, substitute for the variable just solved..

Solve the new equation..

Substitute the value found into any equation involving both variables and solve for the other variable..

What is solving a system by substitution?

The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other.