Question

29) If 2x + 3y = 8 and 4x + 5y = 14, find the value of 3x + 2y.

Answer 1

Answer :

We are given with a pair of simultaneous linear equations where we have to find the value for x and y.

GiveN:

• 2x + 3y = 8
• 4x + 5y = 14

We have to solve for x and y. Then we have to plug these values in order to get 3x + 2y as asked in the Q.

Let,

• 2x + 3y = 8 -------------(1)
• And, 4x + 5y = 14 -----------(2)

Multiplying equation (1) with ×2,

➝ 2(2x + 3y) = 16

Opening the parentheses,

➝ 4x + 6y = 16

Now subtracting equation (2) from equation (1),

➝ 4x + 6y - (4x + 5y) = 16 - 14

➝ 4x + 6y - 4x - 5y = 2

➝ y = 2

Now putting value of y in equation (1),

➝ 2x + 3(2) = 8

➝ 2x + 6 = 8

➝ 2x = 2

➝ x = 1

We have find 3x + 2y for the required values of x and y. So, let's plug in the values to get the required answer:

➝ 3(1) + 2(2)

➝ 3 + 4

➝ 7

So, the required answer of the above Q.,

$\large{ \therefore{ \boxed{ \bf{ \red{7}}}}}$

And we are done !!

Answer 2

We are given with a pair of simultaneous linear equations where we have to find the value for x and y.

$\huge{GiveN:}$

2x + 3y = 8

4x + 5y = 14

We have to solve for x and y. Then we have to plug these values in order to get 3x + 2y as asked in the Q.

$\huge{Let,}$

2x + 3y = 8 -------------(1)

And, 4x + 5y = 14 -----------(2)

Multiplying equation (1) with ×2,

➝ 2(2x + 3y) = 16

Opening the parentheses,

➝ 4x + 6y = 16

Now subtracting equation (2) from equation (1),

➝ 4x + 6y - (4x + 5y) = 16 - 14

➝ 4x + 6y - 4x - 5y = 2

➝ y = 2

Now putting value of y in equation (1),

➝ 2x + 3(2) = 8

➝ 2x + 6 = 8

➝ 2x = 2

➝ x = 1

We have find 3x + 2y for the required values of x and y. So, let's plug in the values to get the required answer:

➝ 3(1) + 2(2)

➝ 3 + 4

➝ 7

So, the required answer of the above Q.,

$\large{ \therefore{ \boxed{ \bf{ \red{7}}}}}$

And we are done !!