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Linear System (2 × 2)

Algebra

Solve two equations in two unknowns with steps.

System of equations

Enter coefficients for the 2×2 linear system.

Equation 1: a₁x + b₁y = c₁

2 x + 3 y = 8

Equation 2: a₂x + b₂y = c₂

1 x − 1 y = 1

Cramer's Rule

D = a₁ b₂ − a₂ b₁2·-1 − 1·3 = -5
Dₓ = c₁ b₂ − c₂ b₁8·-1 − 1·3 = -11
Dᵧ = a₁ c₂ − a₂ c₁2·1 − 1·8 = -6
ClassificationUnique solution
x = Dₓ / D2.2
y = Dᵧ / D1.2

Graphical view

(2.2, 1.2)
Equation 1 Equation 2 Intersection

Frequently asked questions

▶What does the Linear System (2 × 2) do?

The Linear System (2 × 2) is an interactive algebra lab where you change inputs and the answers update live, helping you build intuition without doing the arithmetic by hand.

▶Who should use the Linear System (2 × 2)?

Students from primary to senior secondary classes, parents helping with homework, and anyone revising algebra can use this lab to check answers and explore "what-if" scenarios.

▶Is the Linear System (2 × 2) free to use?

Yes. Every lab on math.suparnpatra.com is free and runs entirely in your browser : nothing is sent to a server.

▶Does the Linear System (2 × 2) work offline?

Once the page is loaded, all calculations run locally in JavaScript, so you can keep using it even on a flaky connection.

▶How accurate are the results?

Results use standard JavaScript double-precision arithmetic and the textbook formula for algebra. We never display scientific notation : numbers are shown as ordinary decimals you can read at a glance.