Question

If the pair of Linear equations x +2y = 3 and 2x + 4y = k are coincide then the
value of 'k'is :​

Answer 1

Answer:

The value of k is 6.

Step-by-step-explanation:

The given linear equations are

x + 2y = 3 - - - ( 1 ) &

2x + 4y = k - - - ( 2 )

We have given that,

The pair of the linear equations are coincide.

We have to find the value of k.

Now,

x + 2y = 3 - - - ( 1 )

Comparing with ax + by = c, we get,

• a₁ = 1
• b₁ = 2
• c₁ = 3

Now,

2x + 4y = k - - - ( 2 )

Comparing with ax + by = c, we get,

• a₂ = 2
• b₂ = 4
• c₂ = k

Now, we know that,

For coincident lines of linear equations,

$\displaystyle{\pink{\sf\:\dfrac{a_1}{a_2}\:=\:\dfrac{b_1}{b_2}\:=\:\dfrac{c_1}{c_2}}}$

$\displaystyle{\implies\sf\:\dfrac{1}{2}\:=\:\dfrac{2}{4}\:=\:\dfrac{3}{k}}$

$\displaystyle{\implies\sf\:\dfrac{1}{2}\:=\:\dfrac{3}{k}}$

$\displaystyle{\implies\sf\:k\:=\:3\:\times\:2}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:k\:=\:6\:}}}}$

∴ The value of k is 6.

Answer 2

$\large{ \underline{ \underline{ \sf{ \color{cyan}{REQUIRED- ANSWER:-}{} }{} }{} }{} }{}$

$\large{ \underline{ \underline{ \sf{ \color{lime}{GIVEN:-}{} }{} }{} }{} }{}$

• The pair of Linear Equations x + 2y = 3 & 2x + 4y =k

• the pair of linear Equations are coincident

• a¹/a² = b¹/b² = c¹/c²

$\large{ \underline{ \underline{ \sf{ \color{lime}{TO - FIND:-}{} }{} }{} }{} }{}$

The Value of K in the Equation.

$\large{ \underline{ \underline{ \sf{ \color{lime}{✓SOLUTION:-}{} }{} }{} }{} }{}$

The Equations x+2y = 3 and 2x + 4y = k

Are coincide,Let us find the value of k

$\sf{ \boxed{ \pink{ \frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} }{} }{} }{}$

Where in the first equation

x + 2y = 3

• a1 = 1
• b1 = 2
• c1 = 3

In the Second Equation,

2x + 4y = k

• a2 = 2
• b2 = 4
• c2 = k

They are coincide therefore,

$\sf{ \rightarrow{ \frac{1}{2} = \frac{2}{4} = \frac{3}{k} }{} }{} \\ \\ \sf{ \rightarrow{ \frac{1}{2} = \frac{3}{k} }{} }{} \\ \\ \boxed{ \rightarrow{ \red{k = 3 \times 2 = 6}{} }{} }{}$

Hence the Value of K is 6.