Question

The pair of linear equations $3x+4y+5=0$ and $12x+16y+15=0$ have:

• A. unique solution
• B. many solutions
• C. no solution
• D. exactly two solutions

Answer 1

Answer: (C)

no solution

Given equations are
$3x+4y+5=0$
$12x+16y+15=0$
The pair of equations are of the form $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$
Here,$a_1=3,b_1=4,c_1=5$ and $a_2=12,b_2=16,c_2=15$
$\Rightarrow \frac{a_1}{a_2}=\frac{3}{12}=\frac{1}{4}$, $\frac{b_1}{b_2}=\frac{4}{16}=\frac{1}{4},\frac{c_1}{c_2}=\frac{5}{15}=\frac{1}{3}$
$\Rightarrow \frac{a_1}{a_2}=\frac{b_2}{b_2}\ne \frac{c_1}{c_2}$
So, the given pair of linear equations are parallel lines and hence will have no solution.