System of linear equations

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Question

If the system of equations $x + 2 y - 3 z = 1,$ $(p + 2) z = 3$ , $(2 p + 1) y + z = 2$ is inconsistent, then the value of $\frac{2020}{500} p =$

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Solution

If $p \neq - 2, \frac{- 1}{2}$ then $z = \frac{3}{p + 2}$ and $y = \frac{1}{p + 2}$
Corresponding to this value we can get ‘ $x$ ’
If $p = \frac{- 1}{2}$ , we get $z = 2$ , thus we get infinite no. of values of $x$ and $y$ .
Thus, $p = - 2$ , the system is inconsistent.
$∴ \frac{2020}{500} p = \frac{2020}{500} (- 2) = - 8.08$

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System of linear equations

Remember concepts with our Masterclasses.

If the system of equations x+2y−3z=1,(p+2)z=3,(2p+1)y+z=2 is inconsistent, then the value of 2020500p=

If p≠−2,−12 then z=3p+2andy=1p+2Corresponding to this value we can get ‘x’If p=−12, we get z=2, thus we get infinite no. of values of xand y.Thus, p=−2, the system is inconsistent.∴2020500p=2020500-2=-8.08

Ready to Test Your Skills?

free study material

If the system of equations $x + 2 y - 3 z = 1,$ $(p + 2) z = 3$ , $(2 p + 1) y + z = 2$ is inconsistent, then the value of $\frac{2020}{500} p =$