observe if lines are parallel or coincident and intersecting x-2y=7 ,x+2y =7
Answers
Answer:
coincident line as all are equal....
Answer :
Intersecting
Note:
★ A linear equation is two variables represent a straight line .
★ The word consistent is used for the system of equations which consists any solution .
★ The word inconsistent is used for the system of equations which doesn't consists any solution .
★ Solution of a system of equations : It refers to the possibile values of the variable which satisfy all the equations in the given system .
★ A pair of linear equations are said to be consistent if their graph ( Straight line ) either intersect or coincide each other .
★ A pair of linear equations are said to be inconsistent if their graph ( Straight line ) are parallel .
★ If we consider equations of two straight line
ax + by + c = 0 and a'x + b'y + c' = 0 , then ;
• The lines are intersecting if a/a' ≠ b/b' .
→ In this case , unique solution is found .
• The lines are coincident if a/a' = b/b' = c/c' .
→ In this case , infinitely many solutions are found .
• The lines are parallel if a/a' = b/b' ≠ c/c' .
→ In this case , no solution is found .
Solution :
Here ,
The given equations are ;
x - 2y = 7
x + 2y = 7
The given equations can be rewritten as ;
x - 2y - 7 = 0 -------(1)
x + 2y - 7 = 0 -------(2)
Now ,
Comparing eq-(1) and eq-(2) with the ax + by + c = 0 and a'x + b'y + c' = 0 , we have ;
a = 1
a' = 1
b = -2
b' = 2
c = -7
c' = -7
Now ,
a/a' = 1/1 = 1
b/b' = -2/2 = -1
c/c' = -7/-7 = 1
Clearly ,
a/a' ≠ b/b'