Question

Form a pair of linear equations for: The sum of the numerator and denominator of the fraction is 3 less than twice the denominator. If the numerator and denominator both are decreased by 1, the numerator becomes half the denominator.

Answer 1

FOR WRITING LINEAR EQUATIONS:

Read the equations carefully to detect the unknowns which are to be found and represent the unknowns by x and y.
Use the conditions given in the problem to frame equations in the unknowns x and y.

SOLUTION:
Let the numerator be 'x’ and denominator be ‘y’.

Condition I:
x +y = 2y -3
x +y -2y = -3
x -y = -3……………….(1)

Condition II:
x -1 = ½( y -1)
2(x-1) = y-1
2x - 2 = y - 1
2x -y = -1 + 2
2x -y = 1………………(2)

HOPE THIS WILL HELP YOU...

Answer 2

Answer:

Step-by-step explanation:

The fraction is 4/7

Step-by-step explanation:

The given problem is on linear equations with two variables say x and y.

Let the fraction required be x/y.

Sum of numerator and denominator = x + y

Given x + y is 3 less than twice the denominator → x + y = 2y - 3

x - y +3 = 0 → (1)

Also, if numerator and denominator are decreased by 1 → (x - 1), (y - 1)

The numerator becomes half of the denominator

x - 1 = \frac{1}{2} (y - 1)x−1=

2

1

​

(y−1)

2x - 2 = y – 1

2x - y =2 -1 =1

2x - y = 1 → (2)

Subtracting (2) and (1) gives x - y + 3 - (2x - y - 1) = 0

x - y + 3 – 2x + y + 1 = 0

-x + 4 =0

x = 4

Substituting x value in (1) gives 4 - y + 3 = 0

y = 7

Therefore x = 4 and y = 7;

The fraction required is 4/7