Advertisements
Advertisements
Question
Find atleast two equations of the straight lines in the family of the lines y = 5x + b, for which b and the x-coordinate of the point of intersection of the lines with 3x − 4y = 6 are integers
Solution
The equations of the given straight lines are
y = 5x + b .......(1)
3x – 4y = 6 .......(2)
To find atleast two equations from the family y = 5x + b for which b is an integer and x-coordinate of the point of intersection of (1) and (2) is an integer.
Solving (1) and (2) using equation (1) inequation (2) (2)
⇒ 3x – 4(5x + b) = 6
3x – 20x – 4b = 6
– 17x = 6 + 4b
x = `(6 + 4"b")/(- 17)`
When b = 7
We have x = `(6 + 28)/(- 17)`
= `34/(- 17)`
= – 2
The corresponding equation of the line is = 5x + 7
When b = – 10
We have x = `(6 - 40)/(- 17)`
= `(- 34)/(- 17)`
= 2
The corresponding equation of the line is y = 5x – 10
Thus y = 5x + 7 and y = 5x – 10 are the two straight lines belonging to the family such that b is an integer and the x-coordinate of the point of intersection with the line (2) is an integer.
APPEARS IN
RELATED QUESTIONS
Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines
Find the distance between the line 4x + 3y + 4 = 0, and a point (−2, 4)
Write the equation of the lines through the point (1, −1) perpendicular to 3x + 4y = 6
If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal
Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and through the point (−1, 2)
Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and perpendicular to x − 2y + 1 = 0
Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from (−10, −2) to the line x + y − 2 = 0
If p1 and p2 are the lengths of the perpendiculars from the origin to the straight lines x sec θ + y cosec θ = 2a and x cos θ – y sin θ = a cos 2θ, then prove that p12 + p22 = a2
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and it passes through the point (5, 3). Find the co-ordinates of the point A
A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq.units
A photocopy store charges ₹ 1.50 per copy for the first 10 copies and ₹ 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying. Draw graph of the cost as x goes from 0 to 50 copies
Find all the equations of the straight lines in the family of the lines y = mx − 3, for which m and the x-coordinate of the point of intersection of the lines with x − y = 6 are integers
Choose the correct alternative:
The point on the line 2x − 3y = 5 is equidistance from (1, 2) and (3, 4) is
Choose the correct alternative:
If a vertex of a square is at the origin and its one side lies along the line 4x + 3y − 20 = 0, then the area of the square is
Choose the correct alternative:
If the lines represented by the equation 6x2 + 41xy – 7y2 = 0 make angles α and β with x-axis then tan α tan β =
