First slide

System of linear equations

Question

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

Moderate

A

1, -2
B

-1, 2
C

1, 2
D

-1, -2

Solution

$x + y + z = 1 - - - - (1)$
$x + 2 y + 4 z = α - - - - - (2)$
$x + 4 y + 10 z = α^{2} - - - - - (3)$
$(2) - (1) \Rightarrow y + 3 z = α - 1$
$(3) - (1) \Rightarrow 3 y + 9 z = α^{2} - 1$
$\begin{array}{l} \Rightarrow 3 (α - 1) = α^{2} - 1 \\ \Rightarrow α^{2} - 3 α + 2 = 0 \\ \Rightarrow (α - 1) (α - 2) = 0 \\ α = 1, 2 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App