Question

For what value of pand q respectively, do the given system of equations have infinitely many solutions?
3x+2y=7
(p+q)x+2py=28​

Answer 1

Answer:

p = 4

q = 8

Step-by-step explanation:

Solution:-

• 3x + 2y = 7

a= 3 ,b = 2 ,c = 7

• (p+q)x + 2py = 28

a' = (p+q) , b' = 2py , c' = 28

Condition for Infinity Many Solution

a/a' = b/b' = c/c'

Now , Comparing we get

→ 3/(p+q) = 2/2p & 2/2p = 7/28

→ 6p = 2(p+q) & 14p = 56

→ 6p = 2(p+q) & p = 56/14

→ 6p = 2(p+q) & p = 4

Hence, p = 4

Substitute the value of p = 4 we get

→ 6×4 = 2(4+q)

→ 24 = 8 + 2q

→ 24-8 = 2q

→ 16 = 2q

→ q = 16/2

→ q = 8

Hence, the value of p = 4 & value of q = 8 .

Answer 2

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p = 4

q = 8

Step-by-step explanation:

Solution:-

• 3x + 2y = 7

a= 3 ,b = 2 ,c = 7

• (p+q)x + 2py = 28

a' = (p+q) , b' = 2py , c' = 28

Condition for Infinity Many Solution

a/a' = b/b' = c/c'

Now , Comparing we get

→ 3/(p+q) = 2/2p & 2/2p = 7/28

→ 6p = 2(p+q) & 14p = 56

→ 6p = 2(p+q) & p = 56/14

→ 6p = 2(p+q) & p = 4

Hence, p = 4

Substitute the value of p = 4 we get

→ 6×4 = 2(4+q)

→ 24 = 8 + 2q

→ 24-8 = 2q

→ 16 = 2q

→ q = 16/2

→ q = 8

Hence, the value of p = 4 & value of q = 8 .

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