Question

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

Answer 1

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

$= > \dfrac{3}{9} \times \dfrac{2}{1}$

$= > \dfrac{6}{9}$

$= > \dfrac{2}{3}$

c1 ÷ c2 = -7/-12

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

Value of "m" = 3

Answer 2

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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

___________________

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

So,

a1 ÷ a2 = 2m

b1 ÷ b2 = 3 ÷ 9/2

=$\dfrac{3}{9} \times \dfrac{2}{1}$

= $\dfrac{6}{9}$

= $\dfrac{2}{3}$

c1 ÷ c2 = -7/-12

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

Value of "m" = 3