solve 1/2x-1/y=-1 , 1/x+1/2x=8 by reducing it to a pair of linear equation
Answers
Step-by-step explanation:
1
Secondary School
Math
5 points
Solve by reducing them to a pair of linear equations. 1/2x + 1/3y =2 and 1/3x + 1/2y = 13/6
Ask for details
Follow
Report
bySwetasingh57 20.08.2019
Answers
rihan99
Virtuoso
Answer:
the value of x=2 and y=3
4.0
3 votes
THANKS 3
Comments
Report
THE BRAINLIEST ANSWER!

ashu3998825
Expert
Answer:
let 1/x = a and 1/y= b
1/2x + 1/3y =2
a/2 + b/3 = 2
3a + 2b = 12 .....…......(1)
1/3x +1/2y =13/6
a/3 + b/ 2 = 13/6
2a +3b = 13 ........…......(2)
from equation (1 ) we have,
a = (12-2b)/3 ...….......(3)
substituting the value of a in equation (2)
2(12-2b)/3 + 3b =13
24 - 4b +9b = 39
5b = 39-24 =15
b = 15/5 = 3
b=3
from equation (3),
a = (12- 2× 3 )/3
a = 6/3 = 2
a=2
1/x = a => 1/a = x
x = 1/2
1/y = b => 1/b = y
y = 1/3
Answer:
The value of x and y is \frac{1}{6}\ {and}\ \frac{1}{4}
6
1
and
4
1
.
To find:
Solve the Equation: \frac{1}{2 x}-\frac{1}{y}=-1 \text { and } \frac{1}{x}+\frac{1}{2 y}=8=?
2x
1
−
y
1
=−1 and
x
1
+
2y
1
=8=?
Solution:
Given: \frac{1}{2 x}-\frac{1}{y}=-1 \text { and } \frac{1}{x}+\frac{1}{2 y}=8
2x
1
−
y
1
=−1 and
x
1
+
2y
1
=8
\frac{1}{2 x}-\frac{1}{y}=-1
2x
1
−
y
1
=−1
\frac{y-2 x}{2 x y}=-1
2xy
y−2x
=−1
y-2 x=-2 x yy−2x=−2xy
2 \mathrm{x}-\mathrm{y}=2 \mathrm{xy} \ldots \ldots \ldots (1)2x−y=2xy………(1)
\frac{1}{x}+\frac{1}{2 y}=8
x
1
+
2y
1
=8
\frac{2 y+x}{2 x y}=8
2xy
2y+x
=8
2 y+x=16 x y2y+x=16xy
x+2 y=16 x y \dots \ldots \ldots \ldots(2)x+2y=16xy…………(2)
Multiplying equation (1) by 2 and then adding it to equation (2), we get
5 \mathrm{x}=20 \mathrm{xy}5x=20xy
y=\frac{1}{4}y=
4
1
Replacing the value of y=\frac{1}{4}y=
4
1
in equation (1),
2 x-y=2 x y2x−y=2xy
2 x-\frac{1}{4}=2 x y2x−
4
1
=2xy
8 x-1=\frac{8 x y}{4}8x−1=
4
8xy
6 \mathrm{x}=16x=1
x=\frac{1}{6}x=
6
1