How do I solve simultaneous equations?

Enter both equations (e.g. 3x + 2y = 8 and 5x − 2y = 16). The solver uses exact arithmetic to find x and y, then shows elimination or substitution steps like in GCSE exams.

What format should I use?

Use ax + by = c (e.g. 2x + 3y = 5) or write one equation with y or x as the subject (e.g. y = 2x − 1). Fractions and decimals are supported.

What if there is no solution?

Parallel lines (same gradient, different intercept) give no solution. The tool will tell you when equations are parallel or when they are the same line (infinitely many solutions).

GCSE revision tools

Simultaneous equations solver

Enter two equations in x and y: two lines (linear), or a line with a circle (x² + y² = r²) or parabola. Exact answers and step-by-step working. Free, no sign-up. More: Factorise quadratics · Expand quadratics · GCSE guide

Simultaneous equations are two equations that must both be true at the same time. For two linear equations, the solution is where the lines cross (one point, none, or infinitely many). For a line and a circle or parabola, substitute the linear equation into the curve — you may get two solution pairs, one, or none. This solver uses exact rational arithmetic where possible. For two lines, choose elimination or substitution; curves always use substitution. Optionally turn on guided practice to answer a question at each step before the working is revealed.

Equation (1)

Equation (2)

Insert:

Method

Eliminate

Automatic y x

Formats: 3x + 2y = 8, y = 2x - 1, x² + y² = 25, y = x². Use fractions (1/2) or decimals (2.5) if needed. One equation must be linear; the other may be a circle or parabola.

Guided practice (optional) — reveal one step at a time and check your understanding before each worked solution is shown