WAEC 2019 · Paper 2 · Q11

(a)
Using determinants, solve the following equations simultaneously:

$5x - 6y + 4z = 15$ $7x + 4y - 3z = 19$ $2x + y + 6z = 46$
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

$\Delta = \begin{vmatrix} 5 & -6 & 4 \\ 7 & 4 & -3 \\ 2 & 1 & 6 \end{vmatrix}$
$= 5(24 + 3) + 6(42 + 6) + 4(7 - 8)$
$= 135 + 288 - 4$
$= 419$ .
Replace the $x$ column by $15, 19, 46$ : $\Delta_x = 15(27) + 6(114 + 138) + 4(19 - 184)$
$= 1257$ .
Replace the $y$ column: $\Delta_y = 5(114 + 138) - 15(48) + 4(322 - 38)$
$= 1676$ .
Replace the $z$ column: $\Delta_z = 5(184 - 19) + 6(322 - 38) + 15(7 - 8)$
$= 2514$ .
So $x = \dfrac{1257}{419} = 3$ , $y = \dfrac{1676}{419} = 4$ and $z = \dfrac{2514}{419} = 6$ .
Check: $15 - 24 + 24 = 15$ ✓, $21 + 16 - 18 = 19$ ✓, $6 + 4 + 36 = 46$ ✓.