Question

4/x+3y=14,3/x-4y=23 find me the answer please ​

Answer 1

x = 1/2

y = 2

Step by step explanation-

$\frac{4}{x} + 3y = 14$

$\frac{3}{x} - 4y = 23$

$Let \: \frac{1}{x} = a$

4a + 3y = 14ㅤ...(1)

3a - 4y = 23ㅤ...(2)

From Eq(1),

4a + 3y = 14

4a = 14 - 3y

$a = ( \frac{14 - 3y}{4} ) \: \: \: \: \: \: \: \: \: ...(3)$

Put the value of a in Eq(2),

$3( \frac{14 - 3y}{4}) - 4y = 23$

$\frac{42 - 9y}{4} - 4y = 23$

$\frac{42 - 9y - 16y}{4}= 23$

$\frac{42 - 25y}{4} = 23$

$42 - 25y = 23 \times 4$

$25y = 92 - 42$

$25y = 50$

$y = \frac{50}{25}$

$\boxed{y = 2}$

Put the value of y in Eq(3),

$a = \frac{14 - 3y}{4}$

$a = \frac{14 - 3 \times 2}{4}$

$a = \frac{14 - 6}{4}$

$a = \frac{8}{4}$

$a = 2$

Now put the value of a = 1/x

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

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

Hope you understand (◍•ᴗ•◍)❤

Answer 2

Given
4/x+3y=14——————(1)
3/x-4y=23——————(2)

Multiply equation(1) by 3 and equation(2) by 4.
= 3*[4/x+3y=14]
=12/x+9y=42 ——————(3)

= 4*[3/x-4y=23]
=12/x-16 y=92 ——————(4)

Solve equations (3) and (4)
12/x-16y=92
12/x+9y=42
- - -
———————
(12/x-12/x)+(-16y-9y)=(92-42)
-25y = 50
y= -2

Put y= -2 in equation (1), we get
4/x+3y=14
4/x+3(-2)=14
4/x-6=14
4/x=14+6
4/x=20
x= 1/5


Hope it will help you.