Draw the graph of the equations x - y +1 = 0 and 3x +2y -12 = 0. Using this graph, find the values of x and y which satisfy both the equations
Answers
EXPLANATION.
Graph of the equations.
⇒ x - y + 1 = 0. - - - - - (1).
⇒ 3x + 2y - 12 = 0. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ x - y + 1 = 0. - - - - - (1).
Put the value of x = 0 in the equation, we get.
⇒ (0) - y + 1 = 0.
⇒ - y + 1 = 0.
⇒ y = 1.
Their Co-ordinates = (0,1).
Put the value of y = 0 in the equation, we get.
⇒ x - (0) + 1 = 0.
⇒ x + 1 = 0.
⇒ x = - 1.
Their Co-ordinates = (-1,0).
From equation (2), we get.
⇒ 3x + 2y - 12 = 0. - - - - - (2).
Put the value of x = 0 in the equation, we get.
⇒ 3(0) + 2y - 12 = 0.
⇒ 2y - 12 = 0.
⇒ 2y = 12.
⇒ y = 6.
Their Co-ordinates = (0,6).
Put the value of y = 0 in the equation, we get.
⇒ 3x + 2(0) - 12 = 0.
⇒ 3x - 12 = 0.
⇒ 3x = 12.
⇒ x = 4.
Their Co-ordinates = (4,0).
Both curves intersects at a point = (2,3).
Put the value of (x, y) = (2,3) in equation (1), we get.
⇒ x - y + 1 = 0.
⇒ 2 - 3 + 1 = 0.
⇒ 3 - 3 = 0.
⇒ 0 = 0.
Put the value of (x, y) = (2,3) in equation (2), we get.
⇒ 3x + 2y - 12 = 0.
⇒ 3(2) + 2(3) - 12 = 0.
⇒ 6 + 6 - 12 = 0.
⇒ 12 - 12 = 0.
⇒ 0 = 0.
Values of the (x, y) = (2,3).
Given :-
x - y + 1 = 0
3x + 2y - 12 = 0
To Find :-
x and y
Solution :-
x - y = 0 - 1
x - y = -1
Putting x as 0
0 - y = -1
-y = -1
y = 1
Coordinates = (0,1)
Putting y = 0
x - 0 = -1
x = -1
Coordinates = (-1,0)
Eq 2
3x + 2y - 12 = 0
3x + 2y = 0 + 12
3x + 2y = 12
Putting x = 0
3(0) + 2y = 12
0 + 2y = 12
2y = 12
y = 12/2
y = 6
Coordinates = (0,6)
Putting y = 0
3x + 2(0) = 12
3x + 0 = 12
3x = 12
x = 12/3
x = 4
Coordinates = (4,0)
Now
Both will intersect at (2,3)
