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

Question:

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

$x+3 y-4=0$

$2 x+6 y=7$

Solution:

The given linear pair of equations are

$x+3 y-4=0$

$2 x+6 y=7$

$a_{1}=1, a_{2}=2, b_{1}=3, b_{2}=6, c_{1}=4, c_{2}=7$

$\frac{a_{1}}{a_{2}}=\frac{1}{2}$

$\frac{b_{1}}{b_{2}}=\frac{3}{6}$

$\frac{b_{1}}{b}=\frac{1}{2}$

$\frac{c_{1}}{c_{2}}=\frac{4}{7}$

If $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ then

$a_{1} b_{2}=a_{2} b_{1}$

$a_{1} b_{3}-a_{2} b_{1}=0$

$1 \times 6-2 \times 3=0$

$6-6=0$

Hence, the number of solutions of the pair of linear equation is 0 .

Therefore, the equations have no solution.

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