Write the number of solution of the following pair of linear equations:

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.

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