Check whether the following pair of linear equation are consistent or inconsistent $3x+2y=5$, $2x−3y=7$.


Given: Pair of the linear equation: $3x+2y=5$, $2x−3y=7$.

To do: To check whether the following pair of linear equation are consistent or inconsistent.

Solution:

Given equations :-

$3x + 2y = 5$ And $2x - 3y = 7$

Here,

$a_1 = 3,\ a_2 = 2,\ b_1 = 2,\ b2 = -3,\ c_1 = 5$ and $c_2 = 7$

Now,

$\frac{a_1}{a_2} = \frac{3}{2}$

$\frac{b1}{b2} = \frac{2}{-3} = -\frac{2}{3}$

$\frac{c_1}{c_2} = \frac{5}{7}$

As we can see that,

$\frac{a_1}{a_2}
eq \frac{b_1}{b_2}$

This pair of equation have only one solution.

Therefore, these equations are consistent.
 

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Updated on: 10-Oct-2022

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