Question 11 Mark
Find whether the lines representing the following pair of linear equation intersect at a point, are parallel or coincident : $\frac{3}{2} x+\frac{5}{3} y=7$ and $\frac{3}{2} x+\frac{2}{3} y=6$
Answer
View full question & answer→Compare given equations with $a x+b y=c$,
$\frac{3}{2} x+\frac{5}{3} y=7$
$\therefore a_1=\frac{3}{2}, b_1=\frac{5}{3}$ and $c_1=7$
$\frac{3}{2} x+\frac{2}{3} y=6$
$\therefore a_2=\frac{3}{2}, b_2=\frac{2}{3}$ and $c_2=6$
Now, $\frac{a_1}{a_2}=\frac{\frac{3}{2}}{\frac{3}{2}}=1$ and $\frac{b_1}{b_2}=\frac{\frac{5}{3}}{\frac{2}{3}}=\frac{5}{2}$
Here, $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
Thus, the lines formed by following pair of linear equation intersect at a point.
$\frac{3}{2} x+\frac{5}{3} y=7$
$\therefore a_1=\frac{3}{2}, b_1=\frac{5}{3}$ and $c_1=7$
$\frac{3}{2} x+\frac{2}{3} y=6$
$\therefore a_2=\frac{3}{2}, b_2=\frac{2}{3}$ and $c_2=6$
Now, $\frac{a_1}{a_2}=\frac{\frac{3}{2}}{\frac{3}{2}}=1$ and $\frac{b_1}{b_2}=\frac{\frac{5}{3}}{\frac{2}{3}}=\frac{5}{2}$
Here, $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
Thus, the lines formed by following pair of linear equation intersect at a point.