× ÷ and full-width input are normalized automatically. Implicit multiplication like 2x or (x+1)(y-1) is supported.
How to use (3 steps)
- Enter two equations (× and full-width text are OK)
- Choose fraction/decimal display, check, and mode
- Switch views: recommended, elimination, substitution, graph
Examples
Result summary
All input and math stay in your browser; nothing is sent to servers.
Elimination is recommended because coefficients align easily.
See how coefficients are aligned to add/subtract and eliminate a variable.
Isolate the simplest variable, substitute with parentheses, and solve.
If there is an intersection, it is the solution. Parallel lines mean no solution; overlapping lines mean infinitely many solutions.
Check
FAQ
When should I pick elimination vs substitution?
If any coefficient is 1 or -1, substitution is simpler. Otherwise, try elimination after aligning coefficients with the least common multiple.
Why is it valid to multiply both equations by the same number?
Doing so does not change the solution set, so clearing denominators or aligning coefficients keeps the answers intact.
Why must I use parentheses when substituting?
Parentheses prevent sign and distribution mistakes. This tool always inserts them before substitution.
How do you detect no solution or infinite solutions?
When the determinant is zero, mismatched constants imply parallel lines (no solution), while matching ratios imply overlapping lines (infinite solutions). The graph reflects the same classification.
Are fraction and decimal answers exact?
Yes. We keep exact rationals internally. Finite decimals are shown precisely; repeating decimals include an ≈ with limited digits.
Is anything sent to servers?
No. Only when you copy a share URL are equations and settings placed into the URL query.
How to solve simultaneous equations with steps and graph
Choose the method from the coefficients
Use substitution when one equation already has a coefficient of 1 or -1, because isolating a variable is quick. Use elimination when the same variable can be cancelled after multiplying one or both equations. The step log shows both the algebra and the reason each operation keeps the solution set unchanged.
Read the graph as a solution check
- One intersection means one ordered pair solves both equations.
- Parallel lines mean the equations have the same slope but different constants, so there is no solution.
- Overlapping lines mean both equations describe the same line, so there are infinitely many solutions.
Fractions, decimals, and common mistakes
Fractions and finite decimals are normalized before solving, so you can enter values like 1/2, -3.5, or 0.25. The most common mistakes are losing a minus sign during substitution, not distributing a multiplier across every term, or comparing rounded decimals instead of the exact rational result.
When to move to another tool
This page is for two linear equations in two variables. Use the graphing calculator when you need function intersections beyond straight lines, or an RREF / matrix tool when you have three or more variables.
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