The graphs of the equations 2x+3y-2=0 and x-2y-8=0 are two lines which are
Answers
Given:
The graphs of the equations 2x+3y-2=0 and x-2y-8=0
To find:
The type of lines.
Solution:
Consider the attached figure while going through the following steps.
From given, we have,
2x + 3y - 2 = 0
x - 2y - 8 = 0
These two lines meet or intersect at a point (4, -2).
Therefore, these system of equations have an unique solution.
These lines are non - parallel and non - perpendicular.
Verification:
If these equations meet at a point, then this point has to satisfy both the equations. So, we have,
2x + 3y - 2 = 0
2 (4) + 3 (-2) - 2 = 0
8 - 6 - 2 = 0
2 - 2 = 0
0 = 0
x - 2y - 8 = 0
4 - 2 (-2) - 8 = 0
4 + 4 - 8 = 0
8 - 8 = 0
0 = 0
Hence verified.
EXPLANATION.
Graph of linear equations.
⇒ 2x + 3y - 2 = 0. - - - - - (1).
⇒ x - 2y - 8 = 0. - - - - - (2).
From equation (1), we get.
⇒ 2x + 3y - 2 = 0. - - - - - (1).
Taking y - axis it means x = 0.
Put the value of x = 0 in the equation, we get.
⇒ 2(0) + 3y - 2 = 0.
⇒ 3y - 2 = 0.
⇒ 3y = 2.
⇒ y = 0.66.
Their Co-ordinates = (0, 0.66).
Taking x - axis it means y = 0.
Put the value of y = 0 in the equation, we get.
⇒ 2x + 3(0) - 2 = 0.
⇒ 2x - 2 = 0.
⇒ 2x = 2.
⇒ x = 1.
Their Co-ordinates = (1,0).
From equation (2), we get.
⇒ x - 2y - 8 = 0. - - - - - (2).
Taking y - axis it means x = 0.
Put the value of x = 0 in the equation, we get.
⇒ (0) - 2y - 8 = 0.
⇒ - 2y - 8 = 0.
⇒ - 2y = 8.
⇒ 2y = - 8.
⇒ y = - 4.
Their Co-ordinates = (0, -4).
Taking x - axis it means y = 0.
Put the value of y = 0 in the equation, we get.
⇒ x - 2(0) - 8 = 0.
⇒ x - 8 = 0.
⇒ x = 8.
Their Co-ordinates = (8,0).
Both curves intersect at the point = (4, -2).
