PrerequisitesPrerequisite

Two-variable systems - elimination

Add or subtract equations to eliminate one variable.

  • Multiply a whole equation if needed to create matching coefficients.
  • Add or subtract to remove one variable, then solve for the other.
  • Substitute back to find the remaining variable and check both original equations.

Example

Eliminate

Solve the system of equations by elimination.

This is equation (1) after dividing every term by .Equation (2): subtract times equation (1) to eliminate .This is equation (2) after dividing every term by .Equation (1): subtract times equation (2) to eliminate .Read each variable and check all values in the original equations.

Remember
If both variables cancel, a false statement means no solution; identical line equations have infinitely many solutions.

Your turn

Question 1

Solve the system.

Check answer
Equation (2): subtract times equation (1) to eliminate .This is equation (2) after dividing every term by .Equation (1): subtract times equation (2) to eliminate .Read each variable and check all values in the original equations.
Question 2

Solve the system.

Check answer
This is equation (1) after dividing every term by .Equation (2): subtract times equation (1) to eliminate .This is equation (2) after dividing every term by .Equation (1): subtract times equation (2) to eliminate .Read each variable and check all values in the original equations.
Question 3

Solve the system.

Check answer
This is equation (1) after dividing every term by .Equation (2): subtract times equation (1) to eliminate .This is equation (2) after dividing every term by .Equation (1): subtract times equation (2) to eliminate .Read each variable and check all values in the original equations.
Question 4

Solve the system.

Check answer
This is equation (1) after dividing every term by .Equation (2): subtract times equation (1) to eliminate .This is equation (2) after dividing every term by .Equation (1): subtract times equation (2) to eliminate .Read each variable and check all values in the original equations.
Question 5

Solve the system.

Check answer
This is equation (1) after dividing every term by .Equation (2): subtract times equation (1) to eliminate .This is equation (2) after dividing every term by .Equation (1): subtract times equation (2) to eliminate .Read each variable and check all values in the original equations.
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