What is the ratio of newspaper readers to magazine readers on Friday?
On which day(s), the difference between the number of newspaper and magazine readers in
the library was maximum?
On which day(s), the difference between the number of newspaper and magazine readers in the library was minimum?
Answers
Answer࿐
Given,
3x+2y = -4 ----------(1)
2x+5y = 1 -----------(2)
¶ Find Point of Intersection of these 2 lines
Do 2×(1) - 3×(2)
6x+4y = -8 ----------(3)
6x+15y = 3 ---------(4)
-----------------------
-11y = -11
=> y = 1
Substitute in (1)
3x+2(1) = -4
=> 3x = -4-2
=> 3x = -6
=> x = -2
•°• Point of Intersection of the lines 3x+2y+4= 0 & 2x+5y-1= 0 is (-2,1)
¶ By using the Slope-Intercept form, find the form of equation of line passing through the point (-2,1)
y = mx + c
substitute x = -2 & y = 1
=> 1 = -2m + c
=> c = 1 + 2m
•°• The Required Equations of straight line is of form :
y = mx + 1 + 2m -----------(5)
¶ The perpendicular distance (or simply distance) 'd' of a point P(x1,y1) from Ax+By+C = 0 is given by
Given,
(x1,y1) = (-2,1) & d = 2
=> (4m+2)² = 2(m² + 1)
=> 16m² + 16m + 4 = 2m² + 2
=> 14m² + 16m + 2 = 0
=> 7m² + 8m + 1 = 0
Factorise the equation
=> 7m² + 7m + m + 1 = 0
=> 7m(m+1) + 1(m+1) = 0
=> (m+1)(7m+1) = 0
=> m = -1 and m = -1/7
Now Substitute m = -1 in (5)
=> y = (-1)x+1+2(-1)
=> y = -x + 1 - 2
=> y = -1 - x
(or)
=> -x - y -1 = 0
=> x + y + 1 = 0 ------------(6)
Substitute m = -1/7 in (5)
=> y = (-1/7)x + 1 + 2(-1/7)
=> y = -x/7 + (7-2)/7
=> y = (-x+5)/7
=> 7y = -x+5
or
=> -x - 7y + 5 = 0
=> x + 7y - 5 = 0 ----------(7)
•°• The Required equation of straight lines are :
x + y + 1 = 0 & x + 7y - 5 = 0
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