The paint of linear equations ax+2y=7 & 3x+by=16 represent parallel lines if
Answers
Answer:
ab = 6
Step-by-step explanation:
For two lines to be parallel, they must have the same slope. So, find the slope of bothe lines and equate them.
Answer :
The given lines will be parallel if ;
• a ≠ 21/16
• b ≠ 32/7
• ab = 6
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 + V = 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 linear equations are ;
ax + 2y = 7
3x + by = 16
The given equations can be rewritten as ;
ax + 2y - 7 = 0
3x + by - 16 = 0
Clearly ,
A = a
B = 2
C = -7
A' = 3
B' = b
C' = -16
The given lines will be parallel if ;
A/A' = B/B' ≠ C/C'
=> a/3 = 2/b ≠ -7/-16
=> a/3 = 2/b ≠ 7/16
• If a/3 ≠ 7/16
→ a ≠ (7/16)×3
→ a ≠ 21/16
• If 2/b ≠ 7/16
→ b ≠ 2×(16/7)
→ b ≠ 32/7
• If a/3 = 2/b
→ ab = 2×3
→ ab = 6