# System of Equations Worksheets

There are two sets of solve systems of equations worksheets:

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 students learn how to solve systems of equations using the substitution method.

### How to solve a system of equations using substitution?

There are three sets of solving systems of equations using substitution.

• Solve System of Equations. (one equation has a variable with a coefficient of 1)
• Solve System of Equations. (unique solution)
• Solve System of Equations. (unique solution, no solution, or infinitely many solutions)

Solving systems of equations involves finding the values of variables that satisfy multiple equations simultaneously. There are several methods to solve systems of equations, including substitution, elimination, graphing, and using matrices. Let’s go through two common methods: substitution and elimination.

Method 1: Substitution

1. Write Down the Equations: Start by writing down the system of equations you want to solve.
2. Isolate a Variable: Choose one equation and isolate one variable in terms of the other variables.
3. Substitute: Substitute the expression you found in step 2 into the other equation(s). This will result in a new equation with only one variable.
4. Solve for the Variable: Solve the equation from step 3 to find the value of the variable.
5. Back-Substitute: Substitute the value of the variable back into the expression you found in step 2 to find the value of another variable.
6. Check Solutions: Substitute the values of the variables into the original equations to ensure they satisfy all the equations.

Method 2: Elimination

1. Write Down the Equations: Start by writing down the system of equations you want to solve.
2. Multiply Equations: If necessary, multiply one or both equations by constants so that the coefficients of one variable are the same in both equations.
3. Add or Subtract Equations: Add or subtract the equations to eliminate one variable. This will result in a new equation with only one variable.
4. Solve for the Variable: Solve the equation from step 3 to find the value of the variable.
5. Substitute: Substitute the value of the variable into one of the original equations to solve for the other variable.
6. Check Solutions: Substitute the values of the variables into the original equations to ensure they satisfy all the equations.

Keep in mind that some systems may have unique solutions, no solution, or infinitely many solutions.

When to use the substitution method and when to use the elimination method.
The choice between using the substitution method or the elimination method to solve a system of equations depends on the specific equations you’re working with and your preference for solving them. Here are some considerations to help you decide which method to use:

• Use the Elimination Method if the coefficients of one variable in both equations are easy to cancel i.e. if the coefficients are already opposites or can be easily made opposites by multiplying one or both equations.
• Use the Substitution Method if one equation has a variable with a coefficient of 1. This will avoid dealing with fractions in the the substitution process.

Have a look at this video if you need to review how to solve Solving Systems of Equations By Elimination & Substitution With 2 Variables.

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Systems of Equations Worksheets.

### More System of Equations Worksheets

Printable
System of Equations Worksheet #1 (one equation has a variable with a coefficient of 1)
System of Equations Worksheet #2 (unique solution)
System of Equations Worksheet #3 (unique solution, no solution, or infinitely many solutions)

More Printable Worksheets

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