Answer :
The value of a and b is 1,-1
What are parallel lines?
⇒ Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. They also have the same slope
Calculation :
We have been given two lines x+y=3 and 2x-3y=1 which intersect at a point
Now we are going to find the point of intersection of these two lines:
⇒ x+y=3
y=3-x
By putting the value of y in another line we will get the point at which both the lines intersect
⇒ 2x-3(3-x)=1
2x-9+3x=1
5x-9=1
5x=10
x=2
⇒ Hence y=1
So the point of intersection of lines x+y=3, and 2x-3y=1 is (2,1)
It is being given that the line x/a+y/b=1 passes through their point of the intersection so the point (2,1) lies on the line x/a+y/b=1
By putting the value of (x,y) in the line
⇒ 2/a+1/b=1 -------- (1)
For any line of the form ax+by+c=0
their slope is =( -coefficient of x)/(coefficient of y)
⇒ slope = -a/b
The slope of x/a+y/b=1 is:
slope (m₁)= -coefficient of x/coefficient of y
=(-1/a)/(1/b)
= -b/a
For line y=x-6
⇒ x-y-6=0
slope(m₂)= -1/-1=1
It is given that both the lines are parallel hence there slopes will be same
Hence m₁=m₂
1=-b/a
⇒ a=-b
By putting the value of a in equation (1)
2/a+1/b=1
2/-b+1/b=1
-2/b+1/b=1
(-2+1)/b=1
⇒ b=-1
On putting the value of b in the equation a=-b we will get the value of a=1
⇒ Hence the values of a and b are 1,-1
Learn more about parallel lines here :
brainly.com/question/12676838
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Disclaimer: The question was given incorrectly on the portal. Here is the correct question
Questions: If the straight line x/a+y/b=1 passes through the point of intersection of the lines x+y=3 and 2x−3y=1 and is parallel to x−y−6=0, find a and b.
