System of Equations Solver $(2×2 / 3×3)$
Algebra, Linear Algebra
Intro: Enter 2 or 3 linear equations with real-number coefficients. We’ll solve and show each elimination/substitution step.
Worked example
- Solve the system: $\begin{cases} 2x + 3y = 7 \\ -x + 4y = 5 \end{cases}$
- Solve the system: $\begin{cases} x + 2y - z = 1 \\ 3x - y + 2z = 12 \\ 2x + y + z = 7 \end{cases}$
- Complete example: $\begin{cases} 2x + 3y = 7 \\ -x + 4y = 5 \end{cases}$
- From $2x + 3y = 7$, express $x = \dfrac{7 - 3y}{2}$.
- Substitute into $-x + 4y = 5 \;\Rightarrow\; -\dfrac{7 - 3y}{2} + 4y = 5$.
- Multiply by $2$: $-(7 - 3y) + 8y = 10 \;\Rightarrow\; -7 + 3y + 8y = 10$.
- Combine: $11y = 17 \;\Rightarrow\; y = \dfrac{17}{11}$.
- Back-substitute: $x = \dfrac{7 - 3\cdot\tfrac{17}{11}}{2} = \dfrac{\tfrac{77}{11} - \tfrac{51}{11}}{2} = \dfrac{\tfrac{26}{11}}{2} = \dfrac{13}{11}$.
- Solution: $\boxed{x=\tfrac{13}{11},\; y=\tfrac{17}{11}}$.
FAQs
Can I mix spaces and semicolons?
Yes—separate equations by commas or semicolons.
Decimals are OK?
Yes, decimals and fractions are both fine.
Why choose Mathix?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
Solve 2x+3y=7 and -x+4y=5
- Express x and substitute into the second equation.
- Get y = 17/11.
- Back-substitute to get x = 13/11.