System of Equations Solver $(2×2 / 3×3)$

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: $\boxed{x=\tfrac{13}{11},\; y=\tfrac{17}{11}}$.

Why choose MathGPT?

• 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.

How this calculator works

• Type or paste your function (LaTeX like \sin, \ln works too).
• Press Generate a practice question button to generate the derivative and the full reasoning.
• Review each step to understand which rule was applied and why.
• Practice with similar problems to lock in the method.

Related

• Quadratic Solver
• Matrix Inverse