Find the values of ‘p’ for which the system of equation + −4=0 and
2 + − 3 = 0, has no solution.
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Answer:
The system of linear equations a
1
x+b
1
y+c
1
= 0 and a
2
x+b
2
y+c
2
= 0 will have a unique solution, if the two lines represented by the equations intersect at a point.
Hence, the lines should not be parallel. i.e., the two lines should have different slopes.
Condition for unique solution is
a2
a1
=
b2
b1
Hence, a
1
=P,b
1
=−1,c
1
=−2
a
2
=6,b
2
=−2,c
2
=−3
Condition for unique solution is
a
2
a
1
=
b
2
b
1
⇒
6
P
=
+2
+1
⇒ P
=
2
6
⇒ P
=3
∴ P can have all real values except 3.
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