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For which value of p and q does the following pair of linear equations have an infinite

number of solutions?

2x + 3y = 7

( p-q ) x + (p+q) y = 3 p + q -2

1 Answer

2 votes

Answer:


p =2.5


q = 0.5

Explanation:

Given


2x + 3y = 7


( p-q ) x + (p+q) y = 3 p + q -2

Required

Find p and q

To do this, we make direct comparison between the given expressions.


2x + 3y = 7 and
( p-q ) x + (p+q) y = 3 p + q -2

This implies that:


(p - q)x = 2x


(p+q)y = 3y


3(p + q) - 2 = 7

So, we have:


p - q = 2 --- (1)


p+q =3 -- (2)


3(p + q) - 2 = 7 --- (3)

If
(1)\ and\ (2) are true, then
(3)\ must be true.

So, we only solve
(1)\ and\ (2)

Add (1) and (2) to eliminate q


p+p-q+q=2+3


2p=5

Solve for p


p = 5/2


p =2.5

Substitute
p =2.5 in (2)


p+q =3


q = 3 - p


q = 3 - 2.5


q = 0.5

User Athan
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