Question

The values of ‘x’ and ‘y’ which satisfy the linear equation 2x + 3y = 16 are.​

Answer 1

Given :- The values of 'x' and 'y' which satisfy the linear equation 2x + 3y = 16 are

A. x = 5, y = 2

B. x = 2, y = 5

C. x= -5, y = -2

D. x= -5, y = 2

Solution :-

checking all options one by one we get,

A) x = 5 , y = 2,

→ 2x + 3y = 16

→ 2 * 5 + 3 * 2 = 16

→ 10 + 6 = 16

→ 16 = 16

→ LHS = RHS .

therefore, value of x = 5 and y = 2 is possible .

A) x = 2 , y = 5,

→ 2x + 3y = 16

→ 2 * 2 + 3 * 5 = 16

→ 4 + 15 = 16

→ 19 ≠ 16

→ LHS ≠ RHS .

therefore, value of x = 5 and y = 2 is not possible .

A) x = -5 , y = -2,

→ 2x + 3y = 16

→ 2 * (-5) + 3 * (-2) = 16

→ (-10) + (-6) = 16

→ (-16) ≠ 16

→ LHS ≠ RHS .

therefore, value of x = 5 and y = 2 is not possible .

A) x = -5 , y = 2,

→ 2x + 3y = 16

→ 2 * (-5) + 3 * 2 = 16

→ (-10) + 6 = 16

→ (-4) ≠ 16

→ LHS ≠ RHS .

therefore, value of x = 5 and y = 2 is not possible .

Hence, Option (A) x = 5, y = 2 is correct answer .

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Answer 2

Given:

The values of ‘x’ and ‘y’ which satisfy the linear equation 2x + 3y = 16.

To find:

The values of x and y.

Solution:

The values of ‘x’ and ‘y’ which satisfy the linear equation 2x + 3y = 16.

Since the options are not given we can do by assuming the values of 'x' or 'y'.

Assume x = 2

2x + 3y = 16

=> 2(2) + 3y = 16

=> 4 + 3y = 16

=> 3y = 12

=> y = 4

2(2) + 3(4) = 16

Hence, the equation satisfied whenx= 2 and y = 4.

Assume y = 2

2x + 3y = 16

=> 2x + 3(2) = 16

=> 2x + 6 = 16

=> 2x = 10

=> x = 5

2(5) + 3(2) = 16

Hence, the equation satisfied when x = 5 and y = 2.

Assume x = 0

2x + 3y = 16

=> 2(0) + 3y = 16

=> 0 + 3y = 16

=> y = 16/3

2(0) + 3(16/3) = 16

Hence, the equation satisfied when x = 0 and y = 16/3.

Assume y = 0

2x + 3y = 16

=> 2x + 3(0) = 16

=> 2x + 0 = 16

=> x = 16/2

=> x = 8

2(8) + 3(0) = 16

Hence, the equation satisfied when x = 8 and y = 0.

Assume x = 6

2x + 3y = 16

=> 2(6) + 3y = 16

=> 12 + 3y = 16

=> 3y = 16 - 12

=> y = 4/3

2(6) + 3(4/3) = 16

Hence, the equation satisfied when x = 6 and y = 4/3.

There exist infinite solutions which satisfy the linear equation 2x + 3y = 16.