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❌ Systems of Equations

Two equations, one answer that satisfies both. See why the point where two lines cross solves both equations at once, and read solutions from a graph.

3
lessons
~15 min
to learn
🔢 Math
subject
Teens
level
Start the course →

What you’ll learn

  1. Two Equations at OnceUnderstand that a system's solution satisfies every equation at once.A system is two or more equations considered together. Each equation alone has many solutions, but the system's solution is the one pair of values that makes them all true. Graphed on the same axes, each equation becomes a line.
  2. Where Lines CrossIdentify the intersection as the solution and recognise special cases.The point where two lines cross lies on both, so its coordinates solve the system. Lines that cross once give one solution, parallel lines give none, and identical lines give infinitely many.
  3. Reading the SolutionRead the solution of a system directly from a graph.To solve graphically, find the intersection, trace down to the x-axis and across to the y-axis to read the coordinates. A crossing at (3, 4) means x = 3 and y = 4 satisfy both equations.

Questions this course answers

A system of equations is:

A system is two or more equations that must hold at once.

Two lines cross at (2, 5). The solution is:

The x-coordinate comes first: x = 2, y = 5.

Two parallel lines that never meet have how many solutions?

Parallel lines never cross, so there is no solution.

Two lines meet at (3, 4). What is the solution?

Read the coordinates directly: x = 3, y = 4.

Grounded in trusted sources

  • Khan Academy — Algebra
  • OpenStax — Elementary Algebra 2e
  • BBC Bitesize — Maths
  • Cuemath — Algebra

Every Wunder lesson is built from real, reputable sources — never invented.

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