Systems Of Equations Elimination Worksheet

Systems of Equations: Elimination Method

When dealing with systems of linear equations, one of the most effective methods for finding the solution is the elimination method. This method involves adding or subtracting the equations in a way that eliminates one of the variables, making it easier to solve for the other variable.

How the Elimination Method Works

The elimination method is based on the principle that if two equations are added or subtracted, the resulting equation is also true. By carefully choosing the equations to add or subtract, we can eliminate one of the variables and solve for the other.

Here’s a step-by-step guide to using the elimination method:

1. Write down the equations: Start by writing down the two equations that make up the system.
2. Make the coefficients the same: Multiply both equations by necessary multiples such that the coefficients of one of the variables (either x or y) are the same.
3. Add or subtract the equations: Add or subtract the two equations to eliminate one of the variables.
4. Solve for the remaining variable: Solve the resulting equation for the remaining variable.
5. Substitute back to find the other variable: Substitute the value of the variable found in step 4 back into one of the original equations to find the value of the other variable.

Example 1: Elimination Method

Solve the following system of equations using the elimination method:

2x + 3y = 7 x - 2y = -3

Step 1: Write down the equations

2x + 3y = 7 x - 2y = -3

Step 2: Make the coefficients the same

Multiply the second equation by 2, so that the coefficients of x are the same:

2x + 3y = 7 2x - 4y = -6

Step 3: Add or subtract the equations

Subtract the two equations to eliminate x:

(2x + 3y) - (2x - 4y) = 7 - (-6) 7y = 13

Step 4: Solve for the remaining variable

Divide both sides by 7 to solve for y:

y = ¹³⁄₇

Step 5: Substitute back to find the other variable

Substitute y = ¹³⁄₇ back into one of the original equations to find x:

2x + 3(¹³⁄₇) = 7 2x + ³⁹⁄₇ = 7 2x = 7 - ³⁹⁄₇ 2x = ³⁴⁄₇ x = ¹⁷⁄₇

📝 Note: Make sure to check your work by plugging the values of x and y back into both original equations.

Example 2: Elimination Method

Solve the following system of equations using the elimination method:

x + 2y = 4 3x - 2y = 5

Step 1: Write down the equations

x + 2y = 4 3x - 2y = 5

Step 2: Make the coefficients the same

No multiplication is needed, as the coefficients of y are already the same.

Step 3: Add or subtract the equations

Add the two equations to eliminate y:

(x + 2y) + (3x - 2y) = 4 + 5 4x = 9

Step 4: Solve for the remaining variable

Divide both sides by 4 to solve for x:

x = ⁹⁄₄

Step 5: Substitute back to find the other variable

Substitute x = ⁹⁄₄ back into one of the original equations to find y:

(⁹⁄₄) + 2y = 4 2y = 4 - ⁹⁄₄ 2y = ⁷⁄₄ y = ⁷⁄₈

Systems of Equations Elimination Worksheet

Here are some practice problems to help you master the elimination method:

Problem 1

Solve the following system of equations using the elimination method:

2x + 5y = 11 x - 3y = -2

Problem 2

Solve the following system of equations using the elimination method:

x + 2y = 5 3x - 2y = 7

Problem 3

Solve the following system of equations using the elimination method:

4x + 2y = 12 x - 3y = -4

Problem 4

Solve the following system of equations using the elimination method:

3x + 4y = 15 2x - 5y = -3

Problem 5

Solve the following system of equations using the elimination method:

x + 3y = 6 2x - 2y = 4

Remember to check your work by plugging the values of x and y back into both original equations.

Related Terms:

• Elimination and substitution worksheet pdf
• System of linear Equations pdf