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System of Linear Equations (Calculation)

Solving for Two Unknowns

When you have two unknown values (like x and y), you need two equations to find their exact values. By combining the equations, we can eliminate one unknown and solve the puzzle.

 x + y = 5
+)x - y = 1
2x     = 6

Examples

  • ・ Addition/Subtraction Method: Add or subtract two equations to eliminate x or y.
  • ・ Substitution Method: Express one variable in terms of the other and substitute it into the other equation.

3 Points for Calculation

1. Match the Coefficients

Multiply the equations so the numbers in front of x (or y) are the same.

2. Eliminate One Variable

Add or subtract the aligned equations. One variable will disappear, leaving a simple linear equation.

3. Find the Second Variable

Once you find the first value, plug it back into either original equation to find the other.

Step-by-Step Solver

① 2x + y = 7
②  x - y = 2
ステップを選択してください

Quick Drill

Solve the following systems of equations.

x + y = 5, x - y = 1
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