solve for X and Y
8/y-3/x=5
6/y-5/x=-2
Answers
Answer:
The value of (x, y) is (3, 2)
The given two equations are
x+\frac{6}{y}=6 \rightarrow(1)x+
y
6
=6→(1)
3 x-\frac{8}{y}=5 \rightarrow(2)3x−
y
8
=5→(2)
The given two equations can be solved using substitution method
Equation (1) can be written as
\frac{1}{y}=\frac{1}{6}(6-x) \rightarrow(3)
y
1
=
6
1
(6−x)→(3)
Substituting equation (3) in equation (2)
3 x-\frac{8}{y}=53x−
y
8
=5
3 x-\frac{1}{y}(8)=53x−
y
1
(8)=5
3 x-8\left(\frac{1}{6}(6-x)\right)=53x−8(
6
1
(6−x))=5
3 x-8+\frac{8 x}{6}=53x−8+
6
8x
=5
3 x+\frac{8 x}{6}=133x+
6
8x
=13
18 x+8 x=7818x+8x=78
26x=7826x=78
x=\frac{78}{26}x=
26
78
x = 3
Substituting the value of x in equation (3)
\frac{1}{y}=\frac{1}{6}(6-x)=\frac{1}{6}(6-3)=\frac{1}{6} \times 3=\frac{1}{2}
y
1
=
6
1
(6−x)=
6
1
(6−3)=
6
1
×3=
2
1
\frac{1}{y}=\frac{1}{2}
y
1
=
2
1
Therefore y = 2
Hence the value of (x, y) is (3, 2).
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