Question

If x=3x+2 and y=2k-1 is a solution of the equation 4x-3y+1=0, find the value of k.​

Answer 1

Correct question :

If x = 3k + 2 and y = 2k - 1 is a solution of the equation 4x - 3y + 1 = 0 , find the value of k.

Answer :

⟹ k = -2

Explanation :

Given :

• x = 3k + 2
• y = 2k - 1
• 4x - 3y + 1 = 0

According to the question :

In this case, we are substituting the values of ' x ' and ' y ' in the equation ' 4x - 3y + 1 = 0 '

Substituting values :

⇛4 ( 3k + 2 ) - 3 ( 2k - 1 ) + 1 = 0

⇛( 12k + 8 ) - ( 6k - 3 ) + 1 = 0

⇛( 12k - 6k ) - ( -3 - 8 ) + 1 = 0

⇛6k + 11 + 1 = 0

⇛6k + 12 = 0

⇛6k = 0 - 12

⇛6k = -12

⇛k = 6 / -12

⇛k = -2

» So, It's Done !! «

Answer 2

Answer :

›»› The value of k = -2

Given :

• x = 3k + 2
• y = 2k - 1

To Find :

• The value of k = ?

Required Solution :

Here in this question, we have to find the value of k So, firstly we have to Both given elements have to be considered as equation 1 and equation 2. And then we have to put the equation 1 and equation 2 into 4x - 3y + 1 = 0. Then, we can frame equation to get the result of x$.$

x = 3k + 2 .....(1)

y = 2k -1 .....(2)

So let's start solving the equation and understand the steps to get our final result for x.

Putting the equation 1 and equation 2 into 4x - 3y + 1 = 0

⇛ 4x - 3y + 1 = 0

⇛ 4(3k + 2) - 3(2k - 1) + 1 = 0

Distribute 4 through the parentheses,

⇛ 12k + 8 - 3(2k -1) +1 = 0

Distribute -3 through the parentheses,

⇛ 12k + 8 - 6k + 3 + 1 = 0

Collect like terms,

⇛ 6k + 8 + 3 + 1 = 0

Calculate the sum of the positive numbers,

⇛ 6k + 12 = 0

Move constant to the right-hand side and change it's sign,

⇛ 6k = -12

Divide both sides of the equation 6,

⇛ k = -2

║Hence, the value of k is -2.║