Question

the pair of equations 5x+3y=6 and 10X+6y=15 has:​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{The given pair of linear equations are:}$

       $5x + 3y = 6$

       $10x + 6y = 15$

       $\text{We must start by finding the values of }\dfrac{a_1}{a_2}, \dfrac{b_1}{b_2}\text{ and }\dfrac{c_1}{c_2}$

       $\text{In our case, }a_1 = 5, a_2 = 10, b_1 = 3, b_2 = 6, c_1 = 6, c_2 = 15$

$\implies \dfrac{a_1}{a_2} = \dfrac{5}{10} = \dfrac{1}{2}$

$\implies \dfrac{b_1}{b_2} = \dfrac{3}{6} = \dfrac{1}{2}$

$\implies \dfrac{c_1}{c_2} = \dfrac{6}{15} = \dfrac{2}{5}$

       $\text{We can see that }\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$

       $\text{We know that if a pair of linear equations have }\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2} \text{ then the}\\\text{pair of linear equations represent parallel lines and have no solution}$

 $\therefore \text{ } \text{ }\boxed{\text{The pair of equations }5x+3y=6 \text{ and } 10x+6y=15 \text{ has no solution}}$