$$1x+2y+1z=2$$, $$3x$$−$$4y$$−$$2z=1$$, and $$2x+5y$$−$$2z=3$$, Then the value of y $$is___________$$.

$$D=1213$$−$$4$$−$$225$$−$$2=45$$, $$D1/x=31212$$−$$4$$−$$225$$−$$2=36$$, $$D1/y=311132$$−$$223$$−$$2=9$$, $$D1/z=31213$$−$$4225$$−$$3=$$−$$9x=54$$, $$y=5$$, $$z=$$−$$5Hence$$ value of y is $$5$$.

System of linear equations

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Question

$\frac{1}{x} + \frac{2}{y} + \frac{1}{z} = 2,$ $\frac{3}{x} - \frac{4}{y} - \frac{2}{z} = 1,$ and $\frac{2}{x} + \frac{5}{y} - \frac{2}{z} = 3,$
Then the value of $y$ is___________.

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Solution

$D = |\begin{matrix} 1 & 2 & 1 \\ 3 & - 4 & - 2 \\ 2 & 5 & - 2 \end{matrix}| = 45,$ $D_{1 / x} = 3 |\begin{matrix} 1 & 2 & 1 \\ 2 & - 4 & - 2 \\ 2 & 5 & - 2 \end{matrix}| = 36,$
$D_{1 / y} = 3 |\begin{matrix} 1 & 1 & 1 \\ 3 & 2 & - 2 \\ 2 & 3 & - 2 \end{matrix}| = 9,$ $D_{1 / z} = 3 |\begin{matrix} 1 & 2 & 1 \\ 3 & - 4 & 2 \\ 2 & 5 & - 3 \end{matrix}| = - 9$
$x = \frac{5}{4}, y = 5, z = - 5$
Hence value of $y$ is $5.$

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System of linear equations

Unlock the full solution & master the concept.

1x+2y+1z=2, 3x−4y−2z=1, and 2x+5y−2z=3, Then the value of y is___________.

D=1213−4−225−2=45, D1/x=31212−4−225−2=36, D1/y=311132−223−2=9, D1/z=31213−4225−3=−9x=54, y=5, z=−5Hence value of y is 5.

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$\frac{1}{x} + \frac{2}{y} + \frac{1}{z} = 2,$ $\frac{3}{x} - \frac{4}{y} - \frac{2}{z} = 1,$ and $\frac{2}{x} + \frac{5}{y} - \frac{2}{z} = 3,$
Then the value of $y$ is___________.