Math

Substitution Method Calculator

Solve a 2×2 linear system by substitution.

a₁

b₁

c₁

a₂

b₂

c₂

Calculated Output

x 1

y 2

Formula: Solve one equation for a variable, substitute into the other

Step-by-Step Breakdown

1. Values used:

2. a₁ = 1

3. b₁ = 2

4. c₁ = 5

5. a₂ = 3

6. b₂ = -1

7. c₂ = 1

9. x = 1

10. y = a₁ x b₁ = 1 x 2 = 2

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The math behind it

From a₁x + b₁y = c₁, express x = (c₁ − b₁y)/a₁, substitute into the second equation and solve for y, then back-substitute for x. The result equals Cramer's rule.

Worked Example

x + 2y = 5 and 3x − y = 1 → x = 1, y = 2.

Frequently Asked Questions

When is substitution easiest?

When one variable already has a coefficient of 1, so isolating it avoids fractions.

The math behind it

Worked Example

Frequently Asked Questions

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