First slide

System of linear equations

Question

The values of $α$ for which the system of equations $x + y + z = 1, x + 2 y + 4 z = a, x + 4 y + 10 z = α^{2}$ is consistent, are given by

Moderate

A

$1, - 2$
B

$- 1, 2$
C

$1, 2$
D

none of these

Solution

Subtracting first equation from the second and third, we get
$y + 3 z = α - 1$
$3 y + 9 z = a^{2} - 1$
$∴ α^{2} - 1 = 3 (α - 1) \Rightarrow α = 1$ or $α = 2$

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