Solve the following system of linear equations graphically and shade the region between the two lines and x-axis.
3x + 2y + 4 = 0
2x-3y-7=0
Answers
EXPLANATION.
Graph of the equation.
⇒ 3x + 2y + 4 = 0. - - - - - (1).
⇒ 2x - 3y - 7 = 0. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ 3x + 2y + 4 = 0. - - - - - (1).
Put the value of x = 0 in the equation, we get.
⇒ 3(0) + 2y + 4 = 0.
⇒ 2y + 4 = 0.
⇒ 2y = - 4.
⇒ y = - 2.
Their Co-ordinates = (0,-2).
Put the value of y = 0 in the equation, we get.
⇒ 3x + 2(0) + 4 = 0.
⇒ 3x + 4 = 0.
⇒ 3x = - 4.
⇒ x = - 4/3.
⇒ x = - 1.33.
Their Co-ordinates = (-1.33,0).
From equation (2), we get.
⇒ 2x - 3y - 7 = 0. - - - - - (2).
Put the value of x = 0 in the equation, we get.
⇒ 2(0) - 3y - 7 = 0.
⇒ - 3y - 7 = 0.
⇒ - 3y = 7.
⇒ 3y = - 7.
⇒ y = - 7/3.
⇒ y = - 2.33.
Their Co-ordinates = (0,-2.33).
Put the value of y = 0 in the equation, we get.
⇒ 2x - 3(0) - 7 = 0.
⇒ 2x - 7 = 0.
⇒ 2x = 7.
⇒ x = 7/2.
⇒ x = 3.5.
Their Co-ordinates = (3.5,0).
Both curves intersects at a point = (0.154, -2.231).
Given :-
3x + 2y + 4 = 0
2x - 3y - 7 = 0
To Find :-
coordinates
Solution :-
3x + 2y + 4 = 0
3x + 2y = 0 - 4
3x + 2y = -4
By putting x = 0
3(0) + 2y = -4
2y = -4
y = -4/2
y = -2
Coordinate = (0,-2)
Now
By putting y = 0
3x + 2(0) = 4
3x + 0 = 4
3x = 4
x = 4/3
Coordinate = (4/3,0)
In 2
2x - 3y - 7 = 0
2x - 3y = 0 + 7
2x - 3y = 7
By putting x = 0
2(0) - 3y = 7
0 - 3y = 7
-3y = 7
y = 7/-3
y = -7/3
Coordinate = (0,-7/3)
By putting y = 0
2x - 3(0) = 7
2x - 0 = 7
2x = 7
x = 7/2
Coordinate = (7/2,0)
Intersection point = (0.154, -2.231).
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