Question

Page following 42) The value of x and y of the following pair of equation is
2/x+3/y=13, 5/x-4/y=-2

A- x=2, y=3
B- x=1/3,y=1/2
C- x=1/2, y=1/3
D- x=3 , y=2
​

Answer 1

Answer:

C-x=1/2,y=1/3

Step-by-step explanation:

apply values in the equation 2/x + 3/y = 13

when x=1/2,y=1/3

LHS = 2/(1/2) + 3/(1/3) = 2(2) + 3(3)

= 4 + 9

= 13 = RHS

5/x - 4/y = -2

LHS = 5/(1/2) - 4/(1/3) = 5(2) - 4(3)

= 10 - 12

= -2 = RHS

Hence, proved :)

Answer 2

Answer:

Value of x is $\frac{1}{2}$and value of y is $\frac{1}{3}$

Step-by-step explanation:

Here given two equations are

$\frac{2}{x} + \frac{3}{y} = 13....(1)$

and

$\frac{5}{x} - \frac{4}{y} = - 2.....(2)$

Let,

$\frac{1}{x} = a \\ \frac{1}{y} = b$

From equation (1),

$2a + 3b = 13.....(3)$

From equation (2),

$5a - 4b = - 2.......(4)$

From equation (3),

$2a + 3b = 13 \\ 2a = 13 - 3b \\ a = \frac{13 - 3b}{2}$

We are putting value of a in equation (4),

$5 \times \frac{13 - 3b}{2} - 4b = - 2 \\ \frac{65 - 15b}{2} - 4b = - 2 \\ \frac{65 - 15b - 8b}{2} = - 2 \\ \frac{65 - 23b}{2} = - 2 \\ 65 - 23b = - 4 \\ 23b = 65 + 4 \\ b = \frac{69}{23} \\ b = 3$

We are putting value of b in equation (3)

$2a + 3 \times 3 = 13 \\ 2a + 9 = 13 \\ 2a = 13 - 9 \\ 2a = 4 \\ a = \frac{4}{2} \\ a = 2$

Now

$a = \frac{1}{x} = 2 \\ x = \frac{1}{2}$

and

$b = \frac{1}{y} = 3 \\ y = \frac{1}{3}$

Required value of x is $\frac{1}{2}$and value of y is $\frac{1}{3}$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

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2) https://brainly.in/question/1169549