Solve the equations: $5 x - 2 y = 6$ and $2 x + 5 y = 3$ and then identify the system of equations.

Consistent

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Inconsistent

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Dependent

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All the above

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Solution

The correct option is A Consistent
The general form for a pair of linear equations in two variables x and y is
$a_{1} x + b_{1} y + c_{1} = 0$ and
$a_{2} x + b_{2} y + c_{2} = 0$
$5 x - 2 y - 6 = 0$ ----- (1)
$2 x + 5 y - 3 = 0$ ----- (2)
Comparing equations 1 and 2 with the general form of equation to write their co-efficient,
$a_{1} = 5; a_{2} = 2; b_{1} = - 2; b_{2} = 5; c_{1} = - 6; c_{2} = - 3$
Compare the ratios of, $\frac{a_{1}}{a_{2}} a n d \frac{b_{1}}{b_{2}}$
$\frac{5}{2} \neq \frac{- 2}{5}$
If $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ , then the pair of linear equations has exactly one solution.
So, the given system of equations is consistent.

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