First slide

System of linear equations

Question

If the system of equations $2 x - 3 y + 4 = 0, 5 x - 2 y - 1 = 0$ and $21 x - 8 y + λ = 0$ is consistent , then $λ$ is

Moderate

A

-1
B

1
C

0
D

-5

Solution

Given system of equation is consistent $\Rightarrow$ Given equations has a solution.
$\begin{aligned} 2 x - 3 y + 4 = 0, 5 x - 2 y - 1 = 0 \Rightarrow x = 1, y = 2 \\ 21 x - 8 y + λ = 0 \Rightarrow 21 - 16 + λ = 0 \Rightarrow λ = - 5 \end{aligned}$

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