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AskSia picks the equation and variable that minimizes algebraic work.
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AI Solver by AskSia
Systems by Substitution Solver: every step shown
Type or photograph the system. AskSia solves one equation for a variable, substitutes into the other, solves the resulting single-variable equation, and back-substitutes for the second variable.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
How does substitution work for systems?
The substitution method solves a system of two equations in two unknowns by isolating one variable in one equation and substituting that expression into the other. Steps: (1) Pick the equation and variable that is easiest to isolate (often a variable with coefficient 1). (2) Solve that equation for that variable in terms of the other. (3) Substitute the expression into the other equation, getting a single-variable equation. (4) Solve for that variable. (5) Back-substitute the solved value to find the first variable.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Systems by Substitution.
Every step transparent, every answer self-checked.
Substitute into the other.
The chosen expression replaces the variable in the second equation.
Substitute
Solve single-variable equation.
Standard linear or quadratic solving with all steps.
Solve
Back-substitute.
Use the solved variable to find the other; verify by substitution.
Complete
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Systems by Substitution problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Systems by Substitution solver covers.
2x2 linear system.
Linear, two equations, two unknowns. Classic substitution.
Linear
Nonlinear systems.
One equation may be quadratic. Substitution still works.
Nonlinear
Word problems.
Translate two relationships into two equations, solve by substitution.
Word problem
Check by graphing.
Solution is the intersection point of two curves.
Graphical
Compare with elimination.
Substitution vs elimination: AskSia chooses based on equation structure.
Method comparison
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
When is substitution easier than elimination?
When one of the equations has a variable with coefficient 1 (or makes one variable easy to isolate), substitution is usually faster. Elimination is faster when both equations have coefficients larger than 1 and the variables are not easily isolated. For nonlinear systems with one variable cleanly isolated, substitution is the natural method. AskSia picks the easier method automatically.
What if substitution leads to a contradiction?
A contradiction (like 0 equals 7) means the system has no solution: the two equations represent parallel lines (in the linear case) that never meet. AskSia recognizes contradictions and reports that the system is inconsistent. The original equations may have a transcription error if a real system is expected to have a solution.
What if substitution gives an identity?
An identity (like 0 equals 0) means the system has infinitely many solutions: the two equations represent the same line. AskSia recognizes this case and parametrizes the solution set: one variable can be chosen freely, and the other is determined by either equation. Infinitely many solutions are reported.
Does substitution work for nonlinear systems?
Yes. For a system with one linear and one nonlinear (quadratic, exponential, etc.) equation, isolate the variable in the linear equation, substitute into the nonlinear, and solve. The result may be a quadratic or higher-degree equation, possibly with multiple solutions. Each solution corresponds to an intersection point of the two curves. AskSia handles nonlinear systems systematically.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
Start Today
Isolate, substitute, solve, back-substitute.
Join 2M+ students using AskSia to solve systems by substitution problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.
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