Substitution Method

System of Equations

Equation 1: x + y =

Equation 2: x + y =

Eq 1: x + 2y = 7 Eq 2: 3x − y = 7

Enter positive or negative integers or decimals. Coefficients and constants can be any real number.

Examples

Solution

Enter your system above and press Solve Using Substitution to see the answer and step-by-step work.

Solution

x = 3, y = 2

(3, 2)

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x =

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y =

What Is the Substitution Method?

Isolate one variable → substitute → solve → back-substitute

The substitution method solves a system of two equations with two unknowns by expressing one variable in terms of the other, then plugging that expression into the second equation — reducing the problem to a single-variable equation you already know how to solve.

Why it works: because both equations must be true at the same time (simultaneously), any value you substitute that satisfies one equation is a valid substitution into the other.

Best used when: one equation already has a variable with coefficient 1 or −1, making isolation clean and fraction-free. For example, x + 2y = 7 easily gives x = 7 − 2y.

Always verify your solution by plugging x and y back into both original equations — a quick sanity check catches arithmetic errors before they count against you on a test.

Substitution vs. Elimination — When to Use Which

Choose substitution when:

A variable already has coefficient 1 or −1 in one equation.
One equation is already solved for a variable (e.g. y = 3x + 1).
The system has only two equations and two unknowns.

Choose elimination when:

Coefficients are large and no variable is easily isolated.
Adding or subtracting the equations directly cancels a variable.
Multiplying one equation by a small number creates equal coefficients.

Both methods always give the same answer — the choice is about which path creates less messy fractions for you.

Systems tripping you up?