For what value of “m” will the pair of linear equations 2x+3y=7 and mx+9/2 y=12,has no solution​

2 thoughts on “For what value of “m” will the pair of linear equations 2x+3y=7 and mx+9/2 y=12,has no solution​”

1. [tex]\huge\bf{{\color{indigo}{G}}{\color{maroon}{í}}{\red{v}}{\color{red}{e}}{\color{orange}{}}{\color{gold}{ñ࿐}}}[/tex]

   In 1st equation,

   2x + 3y – 7 = 0

   a1 = 2

   b1 = 3

   c1 = -7

   ____________________

   In 2nd equation,

   mx + 9/2y -12 = 0

   a2 = m

   b2 = 9/2

   c2 = -12

   ___________________

   [tex]\huge\bf{{\color{indigo}{A}}{\color{maroon}{ñ}}{\red{s}}{\color{red}{w}}{\color{orange}{ê}}{\color{gold}{Я࿐}}}[/tex]

   Divide a1 and a2, b1 and b2, c1 and c2.

   So,

   a1 ÷ a2 = 2m

   b1 ÷ b2 = 3 ÷ 9/2

   =[tex] \dfrac{3}{9} \times \dfrac{2}{1}[/tex]

   = [tex] \dfrac{6}{9}[/tex]

   = [tex] \dfrac{2}{3}[/tex]

   c1 ÷ c2 = -7/-12

   Therefore, Value of m = 3 as a1/a2 = b1/b2

   Value of “m” = 3

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2. Step-by-step explanation:

   TO FIND:-

   The value of m of two equations that had no solution.

   UNDERSTANDING THE CONCEPT:-

   According to the question,

   Has no solution means that the lines are in parallel.

   So, We can find the value of m by dividing both the equations.

   CONCEPT REFRESHER:-

   In 1st equation,

   2x + 3y – 7 = 0

   a1 = 2

   b1 = 3

   c1 = -7

   In 2nd equation,

   mx + 9/2y -12 = 0

   a2 = m

   b2 = 9/2

   c2 = -12

   REQUIRED ANSWER:-

   Divide a1 and a2, b1 and b2, c1 and c2.

   So,

   a1 ÷ a2 = 2m

   b1 ÷ b2 = 3 ÷ 9/2

   [tex] = > \dfrac{3}{9} \times \dfrac{2}{1} [/tex]

   [tex] = > \dfrac{6}{9} [/tex]

   [tex] = > \dfrac{2}{3} [/tex]

   c1 ÷ c2 = -7/-12

   Therefore, Value of m = 3 as a1/a2 = b1/b2

   Value of “m” = 3

   Reply