System of Equations Solver Calculator
Enter two equations (one per line), and this tool will solve the system step-by-step.
Step-by-step method
- Identify the two equations in the system.
- Rewrite both equations in standard form.
- Multiply one equation to match a coefficient.
- Subtract the equations to eliminate one variable.
- Solve for the remaining variable.
- Substitute back to solve for the other variable.
Example 1: x + y = 3; 2x - y = 4
Step 1 - Identify the two equations in the system.
In this problem: These are the two equations in the system.
Step 2 - Rewrite both equations in standard form.
In this problem: Move everything to the left side so each equation equals 0.
Step 3 - Multiply one equation to match a coefficient.
In this problem: Multiply Equation 1 so the coefficient of x matches Equation 2.
Step 4 - Subtract the equations to eliminate one variable.
In this problem: Subtract the equations to eliminate x.
Step 5 - Solve for the remaining variable.
In this problem: Solve for y.
Step 6 - Substitute back to solve for the other variable.
In this problem: Substitute y = 2/3 into an original equation to solve for x.
Final answer: x = 7/3, y = 2/3
Example 2: 3x + 2y = 12; x - y = 1
Step 1 - Identify the two equations in the system.
In this problem: These are the two equations in the system.
Step 2 - Rewrite both equations in standard form.
In this problem: Move everything to the left side so each equation equals 0.
Step 3 - Multiply one equation to match a coefficient.
In this problem: Multiply Equation 1 so the coefficient of x matches Equation 2.
Step 4 - Subtract the equations to eliminate one variable.
In this problem: Subtract the equations to eliminate x.
Step 5 - Solve for the remaining variable.
In this problem: Solve for y.
Step 6 - Substitute back to solve for the other variable.
In this problem: Substitute y = 9/5 into an original equation to solve for x.
Final answer: x = 14/5, y = 9/5
