Question

the pair of equations 5x-15y=8 and 3x-9y=24/5 has(a) one solution (b) two solution (c) Infinitely many solution (d) None of these by solution

Answer 1

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Answer 2

Answer:

The given pair of linear equations are found to have option c) Infinitely many solutions.

Step-by-step explanation:

The given pair of linear equations is:

i) ... $5x-15y=8$

ii)... $3x-9y=\frac{24}{5}$

or we can say:

i) ... $5x-15y-8=0$

ii)... $3x-9y-\frac{24}{5} =0$

By comparing with the general form of pair of linear equations, $a_{1}x+b_1y+c_1=0$  and $a_2x+b_2y+c_2=0$, we get:

$a_1=5\\b_1=-15\\c_1=-8\\a_2=3\\b_2=-9\\c_2=-\frac{24}{5}$

Now, in order to find the nature of solutions for the pair of equations, finding the ratio of the coefficients, we get:

$\frac{a_1}{a_2}=\frac{5}{3}$

$\frac{b_1}{b_2}=\frac{-15}{-9}=\frac{5}{3}$

$\frac{c_1}{c_2}=\frac{-8}{\frac{-24}{5} }=\frac{5}{3}$

Observing the three ratios, we can see that:

$\frac{a_1}{a_2} =\frac{b_1}{b_2} =\frac{c_1}{c_2}$

We know if the three ratios of the corresponding coefficients are all equal to one another, the pair of equations has infinitely many solutions,

Thus, the given pair of equations has infinitely many solutions.