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Systems of two equations

A linear system has two equations and two unknowns. With substitution you solve one equation for one unknown and insert the expression into the other. With elimination you add or subtract the equations so that one unknown disappears. Graphically the solution is the intersection of two straight lines.

\begin{cases} a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 \end{cases}

linear system

Symbols

x,\ y

the unknowns

Example

$x + y = 10$ and $x - y = 4$ . Add them: $2x = 14$ , so $x = 7$ and $y = 10 - 7 = 3$ .

Finally, substitute both values into both equations.

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← Quadratic equations · The square identities →

Part of Mathematics 1T: Algebra and equations.