Discussion

Question:

If the following system of equations have a unique solution what can be said about the value of k?

13x + 91y = 79

23x + ky = 89

Explanation:

Two linear equations:

a₁x + b₁y + c₁ = 0 and
a₂x + b₂y + c₂ = 0

have unique solution when $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

∴ For the given system of equations,

$\frac{13}{23} \neq \frac{91}{k}$

⇒ k ≠ 161

Hence, option (d).

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