Simultaneous Equation Calculator

Solve two linear equations with two unknowns. Enter your own values below to see x and check the method behind it.

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Your inputs

Change the example values to match your situation.

Your result

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Fill in your inputs and select Calculate.
Your result and breakdown will appear here.

How this calculator works

Solve two simultaneous linear equations using their determinant (Cramer’s rule).

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What is Simultaneous Equation Calculator?

Simultaneous Equation Calculator helps you solve two linear equations with two unknowns.

The main result is x, with a breakdown of y. The formula, example and assumptions below explain how to interpret it.

How to use Simultaneous Equation Calculator

Use the example to get familiar with the form, then enter your own figures. Any rates in the example are illustrative. Check the field labels and units before calculating.

  1. Gather first equation: x coefficient, first equation: y coefficient, first equation: right-hand side, second equation: x coefficient, second equation: y coefficient and second equation: right-hand side. Use values from the same situation or reporting period.
  2. Replace the example first equation: x coefficient with your own value, then complete the other fields. Check the displayed units.
  3. Select Calculate and read x with its result breakdown. Change one input and calculate again to compare a second scenario. Reset restores the original example.
  • Enter first equation: x coefficient, at least -1000000. Decimals are accepted.
  • Enter first equation: y coefficient, at least -1000000. Decimals are accepted.
  • Enter first equation: right-hand side, at least -1000000. Decimals are accepted.
  • Enter second equation: x coefficient, at least -1000000. Decimals are accepted.
  • Enter second equation: y coefficient, at least -1000000. Decimals are accepted.
  • Enter second equation: right-hand side, at least -1000000. Decimals are accepted.

Simultaneous Equation Calculator: a worked example

With the inputs below, the result is 3 (x). Follow the example, then replace these illustrative values with your own.

Example inputs and output
Input or outputExample value
First equation: x coefficient2
First equation: y coefficient1
First equation: right-hand side7
Second equation: x coefficient1
Second equation: y coefficient-1
Second equation: right-hand side2
x3
y1

Understanding the Simultaneous Equation result

Read x alongside y. These describe different parts of the same calculation.

Displayed results use a readable number of decimal places. When checking a result by hand, keep extra precision until the last step. To compare scenarios, change one input at a time and keep the others fixed.

  • Example y: 1

Simultaneous Equation Calculator: assumptions and common mistakes

A useful estimate starts with the right inputs. Check the following assumptions and limits before applying the result to your situation.

  • Check the base value, sample definition and chosen operation. Display rounding should come after the calculation.

For wider guidance, visit NIST statistical handbook. The formula and scope of this specific tool are stated on this page.

Simultaneous Equation Calculator FAQs

What does Simultaneous Equation Calculator calculate?

Simultaneous Equation Calculator helps you solve two linear equations with two unknowns. Its main output is x.

What inputs do I need for Simultaneous Equation Calculator?

You need first equation: x coefficient, first equation: y coefficient, first equation: right-hand side, second equation: x coefficient, second equation: y coefficient and second equation: right-hand side. Use the field labels and units to match your figures to the formula.

Which formula does Simultaneous Equation Calculator use?

Solve two simultaneous linear equations using their determinant (Cramer’s rule).

What is a worked example for Simultaneous Equation Calculator?

Example inputs: First equation: x coefficient: 2; First equation: y coefficient: 1; First equation: right-hand side: 7; Second equation: x coefficient: 1. Keep the remaining inputs as shown in the worked-example table. The result is 3 (x).

How should I enter first equation: x coefficient?

Enter first equation: x coefficient, at least -1000000. Decimals are accepted.

How do I choose first equation: y coefficient?

Enter first equation: y coefficient, at least -1000000. Decimals are accepted. The example uses 1; replace it if your circumstances differ.

How should I read x?

Read x alongside y. These describe different parts of the same calculation.

Why might my Simultaneous Equation Calculator result differ from my records?

Check the base value, sample definition and chosen operation. Display rounding should come after the calculation. Differences in entered values, units or rounding can also change the comparison.

Can I compare two scenarios in Simultaneous Equation Calculator?

Yes. Note your first x, change first equation: x coefficient or another input, and select Calculate again. Editing a field clears the old result so it is not mistaken for a new calculation.

Is Simultaneous Equation Calculator free, and where are my inputs calculated?

This calculator is free to use without signing in. Its formula runs in your browser; calculator inputs are not sent to a calculation API. The inputs reset to the example values when you reset the form or start a fresh page.