Question

check whether the number of solutions of 2x+3y = 12
and 3x + 2y = 13 are infinity or
or not. Give reasons.
​

Answer 1

Answer:

condition for infinite solution

are coincident lines ( lines which overlap each other )

or

$\frac{a1}{a2} = \frac{b2}{b2} = \frac{c1}{c2} \\ \frac{a1}{a2} = \frac{2}{3} \\ \frac{b2}{b2} = \frac{3}{2 } \\ \frac{c1}{c2} = \frac{12}{13}$

now we can find that

$\frac{a1}{a2} \: not \: equal \ \frac{b2}{b2} \: not \: equal \ \frac{c1}{c2}$

so the pairs of equation will have only unique solution or finite solution

hope it help

Answer 2

Step-by-step explanation:

Answer:

condition for infinite solution

are coincident lines ( lines which overlap each other )

or

\begin{gathered} \frac{a1}{a2} = \frac{b2}{b2} = \frac{c1}{c2} \\ \frac{a1}{a2} = \frac{2}{3} \\ \frac{b2}{b2} = \frac{3}{2 } \\ \frac{c1}{c2} = \frac{12}{13} \\ \end{gathered}

a2

a1

=

b2

b2

=

c2

c1

a2

a1

=

3

2

b2

b2

=

2

3

c2

c1

=

13

12

now we can find that

\frac{a1}{a2} \: not \: equal \ \frac{b2}{b2} \: not \: equal \ \frac{c1}{c2}

a2

a1

notequal

b2

b2

notequal

c2

c1

so the pairs of equation will have only unique solution or finite solution

hope it help