Linear system
A set of equations where each unknown appears only to the first power, such as x + y = 5 and x - y = 1. A solution makes every equation true at once.
Last updated
Analogy
Two clues about two mystery numbers, which together pin them down.
Example
Add the equations: 2x = 6.So x = 3.Then y = 5 - 3 = 2.Check: 3 - 2 = 1. Correct.
In practice
Models circuits, budgets, mixtures and balancing problems.
Practice
Flashcards
- Solve x + y = 5 and x - y = 1.x = 3, y = 2.
Interview questions
- Explain the three possible outcomes for the number of solutions to a linear system with an example of each.
- One solution: lines cross once
- None: parallel lines, a row 0 = non-zero
- Infinitely many: same line, a free variable
- Elimination reveals which case occurs
Questions people ask
What does linear mean in a linear system?
Each unknown appears on its own, to the first power, multiplied only by a number. Terms such as x squared, xy, or sine of x make the equation non-linear. Linear equations in two unknowns graph as straight lines, hence the name.
How do I solve a system by elimination?
Combine equations to remove one unknown. For x plus y equals 5 and x minus y equals 1, adding gives 2x equals 6. Solve that, then substitute back to find the other unknown. Always check your answer in both original equations.