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Algebra — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSAlgebra2 Marks
Question
Find the values of $x , y , z$ if $\left[\begin{array}{c}x \\ y-z \\ z+3\end{array}\right]+\left[\begin{array}{l}y \\ 4 \\ 3\end{array}\right]=\left[\begin{array}{c}4 \\ 8 \\ 16\end{array}\right]$
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Answer

$ \begin{aligned} & {\left[\begin{array}{c} x \\ y-z \\ z+3 \end{array}\right]+\left[\begin{array}{l} y \\ 4 \\ 3 \end{array}\right]=\left[\begin{array}{c} 4 \\ 8 \\ 16 \end{array}\right]} \\\end{aligned} $
$x+y=4 \ldots(1)$
$ y-z+4=8 \ldots(2)$
Substitute the value of $z$ in $(2)$
$(2) \Rightarrow y-10=4$
Substitute the value of $y$ in $(1)$
$ z+3+3=16$
$ z+6=16$
$ z=16-16=10$
$ y=14$
$ (1) \Rightarrow x+14=4$
$x-4-14=-10$
The value of $x = – 10, y = 14$ and $z = 10$

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