Question

$A_{1}x+B_{1}y+C_1=0$, $A_{2}x+B_{2}y+C_2=0$is a system of two simultaneous linear equations, if $\left(\frac{A_1}{A_2}\right)=\left(\frac{B_1}{B_2}\right)=\left(\frac{C_1}{C_2}\right)$ then the system has ________ solution.

Answer 1

Recall the condition for a pair of equation to have infinitely many solutions

According to the question,

$A_{1}x+B_{1}y+C_1=0$, $A_{2}x+B_{2}y+C_2=0$is a system of two simultaneous linear equations, if $\left(\frac{A_1}{A_2}\right)=\left(\frac{B_1}{B_2}\right)=\left(\frac{C_1}{C_2}\right)$ then the system has infinitely many solution.

Hence, $A_{1}x+B_{1}y+C_1=0$, $A_{2}x+B_{2}y+C_2=0$ has infinitely many solution.