Question

1. Comment on the solvability of the following systems of equations:

- 5x + y = 23 ,

17x + 8 - 3y = 0


Class 10

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Answer 1

Hi,

There are two conditions of solvability

1) Having unique solution

2) Having infinite solution

These conditions can be checked by coefficient of x and y of both the equations

1) Condition for unique solution:

$\frac{a1}{a2} \: \: not \: = \frac{b1}{b2} \: \: \\ \frac{ - 5}{17} \: \: not \: equal \: to \: \frac{ - 1}{3}$
this condition holds true, so the given equation has unique solution.

2) Condition for infinite solution:

$\frac{a1}{a2} \: = \frac{b1}{b2} \: = \frac{c1}{c2}$
hope it helps you.