Question:
Write the number of solution of the following pair of linear equations:
$x+2 y-8=0$
$2 x+4 y=16$
Solution:
The given equations are
$x+2 y-8=0$
$2 x+4 y-16=0$
$a_{1}=1, a_{2}=2, b_{1}=2, b_{2}=4, c_{1}=8, c_{2}=16$
$\frac{a_{1}}{a_{2}}=\frac{1}{2} ; \frac{b_{1}}{b_{2}}=\frac{2}{4} ; \frac{c_{1}}{c_{2}}=\frac{8}{16}$
$\frac{a_{1}}{a_{2}}=\frac{1}{2} ; \frac{b_{1}}{b_{2}}=\frac{1}{2} ; \frac{c_{1}}{c_{2}}=\frac{1}{2}$
$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$
Every solution of the second equation is also a solution of the first equation.
Hence, there are infinite-solution, the system equation is consistent.