The pair of equations 2px+5y=7
&6x-5y=11 has an unique solution. Then value of p will be???
Answers
Step-by-step explanation:
2px+5y=7. x=7-5y/2p
6x-5y=11
-5y=11-6x
5y=-11+6x
2px+(-11+6x)=7
2px-11+6x=7
(2p+6)x=11+7
(2p+6)7-5y/2p=18
2p+6*7-5y=36p
14p-10yp+42-30y=36p
Answer:
p ≠ 3
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 ;
2px + 5y = 7
6x - 5y = 11
The given equations can be rewritten as ;
2px + 5y - 7 = 0
6x - 5y - 11 = 0
Clearly ,
a = 2p , b = 5 , c = -7
a' = 6 , b = -5 , c = -11
Now,
a/a' = 2p/6 = p/3
b/b' = 5/-5 = -1
c/c' = -7/-11 = 7/11
Now,
We know that , for unique solution ;
=> a/a' ≠ b/b'
=> p/3 ≠ -1
=> p = -1×3
=> p ≠ -3