Substitution Method Calculator

Form

Results

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What is Substitution Method?

Solve two simultaneous linear equations for a shared pair of values.

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How to Use This Calculator

  1. Enter or select a1, b1, c1, a2, b2. Complete any remaining fields required by your chosen method.
  2. Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
  3. Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
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Formula Used

a₁x+b₁y=c₁; a₂x+b₂y=c₂
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Variables Explained

InputWhat it means
a1A value or coefficient in the formula above; keep the displayed position and sign.
b1A value or coefficient in the formula above; keep the displayed position and sign.
c1A value or coefficient in the formula above; keep the displayed position and sign.
a2A value or coefficient in the formula above; keep the displayed position and sign.
b2A value or coefficient in the formula above; keep the displayed position and sign.
c2A value or coefficient in the formula above; keep the displayed position and sign.
Precision of calculationsRequested number of output decimal places; this changes display rounding, not input accuracy.
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Worked Example

x+y=5 and x−y=1 give x=3 and y=2.

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Why Use This Calculator?

Solve for two linked unknowns and check them in both original equations.

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Common Mistakes

    • Parallel lines have no unique solution; identical equations have infinitely many.
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Frequently Asked Questions

Should I round numbers before calculating?

Keep the original input precision through the calculation and round the final answer to the precision you need. Rounding an intermediate result can change later steps.

Why can a manual calculation differ slightly?

Check the operation, units, signs and rounding first. Equivalent fractions or expressions can look different while representing the same value.

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Sources & References