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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