Question

For a pair of linear equations
$a_{1}x+b_1+c_1=0$ and $a_{2}x+b_2+c_2=0$
$a_1=12,b_1=2,c_1=6$ and $a_2=24,b_2=4,c_2=7$.
Find the number of solutions the pair of equations will have.

• A. One solution
• B. Infinite solutions
• C. Two solutions
• D. No solution

Answer 1

The correct option is D

No solution

For a pair of linear equations $a_{1}x+b_1+c_1=0$ and $a_{2}x+b_2+c_2=0$, when $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$, there is no solution as the lines that represent these equations are parallel to each other.

Here, $\frac{12}{24}=\frac{2}{4}\ne \frac{6}{7}$

$\Rightarrow$$\frac{1}{2}=\frac{1}{2}\ne \frac{6}{7}$

Therefore, there is no solution for the given pair of linear equation.