solve the following pair of equation by reducing them of a pair of linear equations 5/x-1=2 +1/y-2 -3/y-2=1
Answers
The set of equation is given as,
x−1
5
+
y−2
1
=2
5(y−2)+1(x−1)=2(x−1)(y−2)
5y−10+x−1=2(xy−2x−y+2)
5y+x−11=2xy−4x−2y+4
5y+x−11+4x+2y−4−2xy=0
5x+7y−2xy=15 (1)
And,
x−1
6
−
y−2
3
=1
6(y−2)−3(x−1)=1(x−1)(y−2)
6y−12−3x+3=xy−2x−y+2
6y−3x−9−xy+2x+y−2=0
−x+7y−xy−11=0
x−7y+xy+11=0
x−7y+xy=−11 (2)
Adding equation (1) and equation(2),
6x−xy=4
x(6−y)=4
x=
6−y
4
Substituting the value of x in equation (1),
5(
6−y
4
)+7y−2y(
6−y
4
)=15
6−y
20
+7y−
6−y
8y
=15
20+7y(6−y)−8y=15(6−y)
20+42y−7y
2
−8y=90−15y
7y
2
−49y+70=0
y
2
−7y+10=0
y
2
−5y−2y+10=0
y(y−5)−2(y−5)=0
(y−2)(y−5)=0
y=2,5
At y=2, the equation is undefined, so the only value of y is 5.
Now, substitute the value of y in x=
6−y
4
.
x=
6−5
4
x=
1
4
x=4
Therefore, the values are x=4 and y=5.
I hope this helps you