First slide

System of linear equations

Question

Solution of the system of equations $\frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4,$ $\frac{4}{x} - \frac{6}{y} + \frac{5}{z} = 1,$ $\frac{6}{x} + \frac{9}{y} - \frac{20}{z} = 2, (x, y, z) =$

Moderate

A

$(1, 2, 3)$
B

$(2, 3, 5)$
C

$(3, 2, 5)$
D

$(5, 3, 2)$

Solution

$A u g m e n t e d m a t r i x = [\begin{matrix} 2 & 3 & 10 & 4 \\ 4 & - 6 & 5 & 1 \\ 6 & 9 & - 20 & 2 \end{matrix}] R_{2} \to R_{2} - 2 R_{1}, R_{3} \to R_{3} - 3 R_{1} ~ [\begin{matrix} 2 & 3 & 10 & 4 \\ 0 & - 12 & - 15 & - 7 \\ 0 & 0 & - 50 & - 10 \end{matrix}] T h i s i s e q u i v a l e n t t o t h e s y s t e m o f e q u a t i o n s \frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4, - \frac{12}{y} - \frac{15}{z} = - 7, - \frac{50}{z} = - 10 S o l v i n g t h e a b o v e w e g e t, z = 5, y = 3 a n d x = 2 . ∴ (x, y, z) = (2, 3, 5)$

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