Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 32x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the Y-axis.
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Answers
EXPLANATION.
Graphically the pair of equations.
⇒ 3x - 2y + 2 = 0. - - - - - (1).
⇒ 32x - y + 3 = 0. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ 3x - 2y + 2 = 0. - - - - - (1).
Put the value of x = 0 in the equation, we get.
⇒ 3(0) - 2y + 2 = 0.
⇒ - 2y + 2 = 0.
⇒ 2y = 2.
⇒ y = 1.
Their Co-ordinates = (0,1).
Put the value of y = 0 in the equation, we get.
⇒ 3x - 2(0) + 2 = 0.
⇒ 3x + 2 = 0.
⇒ 3x = - 2.
⇒ x = - 0.66.
Their Co-ordinates = (-0.66,0).
From equation (2), we get.
⇒ 32x - y + 3 = 0. - - - - - (2).
Put the value of x = 0 in the equation, we get.
⇒ 32(0) - y + 3 = 0.
⇒ - y + 3 = 0.
⇒ y = 3.
Their Co-ordinates = (0,3).
Put the value of y = 0 in the equation, we get.
⇒ 32x - (0) + 3 = 0.
⇒ 32x + 3 = 0.
⇒ 32x = - 3.
⇒ x = - 3/32.
⇒ x = - 0.09375.
Their Co-ordinates = (-0.09375,0).
Both curves intersects at a point = (-0.066,0.902).
As we can see that both the lines are intersects it means it is consistent.
Graph of equation y-axes.
⇒ Line : 3x - 2y + 2 = 0 ⇒ (0,1).
⇒ Line : 32x - y + 3 = 0 ⇒ (0,3).
Given :-
3x - 2y + 2 = 0
32x - y + 3 = 0
To Find :-
Coordinate
Solution :-
In Eq 1
3x - 2y + 2 = 0
3x - 2y = 0 - 2
3x - 2y = -2
Putting x as 0
3(0) - 2y = -2
- 2y = -2
y = -2/-2
y = 2/2
y = 1
Coordinate = (0,1)
By putting y as 0
3x - 2(0) = -2
3x - 0 = -2
3x = -2
x = -2/3
Coordinate = (-2/3,0)
In Eq 2
32x - y + 3 = 0
32x - y = 0 - 3
32x - y = -3
Putting x as 0
32(0) - y = -3
0 - y = -3
- y = - 3
y = 3
Coordinate (0,3)
Putting y as 0
32x - 0 = - 3
32x = -3
x = -3/32
Coordinate (-3/32,0)
Meeting point = (0,1) in Eq 1 and (0,3) in Eq 2
Intersection point - (2/3, -3/32)