Question

Question 3 (iv)
On comparing the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$ find out whether the following pair of linear equations are consistent, or inconsistent.
5x - 3y= 11 ; -10x+ 6y= -22

Answer 1

The given equations are 5x - 3y = 11 and -10x + 6y = -22
They can be written as 5x - 3y - 11 = 0 and -10x + 6y + 22 = 0

Comparing these equations with $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$, we get:$a_1=5,b_1=-3,and{c}_1=-11$
$a_2=-10,b_2=6and{c}_2=22$

$\frac{a_1}{a_2}=\frac{5}{-10}=\frac{-1}{2}$

$\frac{b_1}{b_2}=\frac{-3}{6}=\frac{-1}{2}$ and

$\frac{c_1}{c_2}=\frac{11}{-22}=\frac{-1}{2}$

Hence, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
Therefore, these linear equations represent a coincident pair of lines and thus have infinite number of possible solutions.
Hence, the pair of linear equations is consistent.