Solve graphically the pair of equations 2x + 3y =11 and 2x - 4y = -24. Hence find the
value of m, given that the line represented by y = mx + 3 passes through the intersection of
the given pair
Answers
EXPLANATION.
Solve graphically the pair of equations.
⇒ 2x + 3y = 11. - - - - - (1).
⇒ 2x - 4y = - 24. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ 2x + 3y = 11. - - - - - (1).
Put the value of x = 0 in the equation, we get.
⇒ 2(0) + 3y = 11.
⇒ 3y = 11.
⇒ y = 11/3.
⇒ y = 3.66.
Their Co-ordinates = (0,3.66).
Put the value of y = 0 in the equation, we get.
⇒ 2x + 3(0) = 11.
⇒ 2x = 11.
⇒ x = 11/2.
⇒ x = 5.5.
Their Co-ordinates = (5.5,0).
From equation (2), we get.
⇒ 2x - 4y = - 24. - - - - - (2).
Put the value of x = 0 in the equation, we get.
⇒ 2(0) - 4y = - 24.
⇒ - 4y = - 24.
⇒ 4y = 24.
⇒ y = 6.
Their Co-ordinates = (0,6).
Put the value of y = 0 in the equation, we get.
⇒ 2x - 4(0) = - 24.
⇒ 2x = - 24.
⇒ x = - 12.
Their Co-ordinates = (-12,0).
Both curves intersects at a point = (-2,5).
To find value of m.
⇒ y = mx + 3.
Put the value of (x, y) = (-2, 5) in the equation, we get.
⇒ (5) = m(-2) + 3.
⇒ 5 = -2m + 3.
⇒ 5 - 3 = - 2m.
⇒ 2 = - 2m.
⇒ m = - 1.
Given :-
2x + 3y = 11
2x - 4y = -24
To Find :-
Value of m
Solution :-
From 1
2x + 3y = 11
Putting x as 0
2(0) + 3y = 11
3y = 11
y = 11/3
Co-ordinates = (0,11/3)
Putting y as 0
2y + 3(0) = 11
2y = 11
y = 11/2
Co-ordinates = (11/2,0)
From 2
Putting x as 0
2(0) - 4y = -24
0 - 4y = -24
-4y = -24
y = -24/-4
y = 24/4
y = 6
Co-ordinates = (0,6)
Putting y as 0
2x - 4(0) = -24
2x - 0 = -24
2x = -24
x = -24/2
x = -12
Co-ordinate = (-12,0)
Intersection point = (-2,5)
y = mx + 3
5 = m(-2) + 3
5 = -2m + 3
5 - 2 = -2m
2 = -2m
2/-2 = m
1/-1 = m
-1/1 = m
-1 = m
