The pair of equations $2 x+y=5,3 x+2 y=8$ has (a) a unique solution (b) two solutions (c) no solution. (d) infinitely many solutions

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The pair of equations $2 x+y=5,3 x+2 y=8$ has
(a) a unique solution
(b) two solutions
(c) no solution.
(d) infinitely many solutions

The pair of equations $2 x+y=5,3 x+2 y=8$ has
(a) a unique solution
(b) two solutions
(c) no solution.
(d) infinitely many solutions

Answer: (a) a unique solution

Solution:
The given system can be written as:
$2 x+y-5=0$ and $3 x+2 y-8=0$
Given equations are of the following form:
$a_{1} x+b_{1 Y}+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$
Here, $a_{1}=2, b_{1}=1, c_{1}=-5$ and $a_{2}=3, b_{2}=2$ and $c_{2}=-8$
$\therefore \frac{a_{1}}{a_{2}}=\frac{2}{3}, \frac{b_{1}}{b_{2}}=\frac{1}{2}$ and $\frac{c_{1}}{c_{2}}=\frac{-5}{-8}=\frac{5}{8}$
$\therefore \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Given system has a unique solution.
As a result, the lines intersect at one point.