Solve a linear equation

A standard method from Number and algebra basics: the steps and worked examples.

Steps

Expand brackets.
Move x-terms to one side and numbers to the other. Change the sign when a term crosses the "=".
Divide by the coefficient of x.
Check by substituting back.

Why: an equation is a balance; whatever you do to one side, do to the other.

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Worked examples

Example 1: Solve the linear equation 3(x − 2) = x + 8.

3x − 6 = x + 8      expand
3x − x = 8 + 6      move terms
    2x = 14
     x = 7          check: 3(5) = 15 = 7 + 8 ✓

Example 2: Solve the simultaneous equations 2x + 3y = 12 and x − y = 1 (substitution).

x = y + 1                      from the second equation
2(y + 1) + 3y = 12             substitute
       5y + 2 = 12
            y = 2,  x = 3      check: 2(3) + 3(2) = 12 ✓, 3 − 2 = 1 ✓

Example 3: Solve the simultaneous equations 3x + 2y = 16 and 5x − 2y = 8 (elimination).

(3x + 2y) + (5x − 2y) = 16 + 8      add: the y-terms cancel
                   8x = 24
                    x = 3
3(3) + 2y = 16                      substitute back
       2y = 7
        y = 3.5                     check: 5(3) − 2(3.5) = 15 − 7 = 8 ✓

For the whole topic, read Number and algebra basics: key points, common mistakes and how the DSE tests it.

Steps

Worked examples

Other methods in this topic