Question

If the system of equations 2x + 3y = 7 and, (a + b) x + (2a - b) y = 21 has many solutions, then
(a) a = 1, b = 5
(b) a = 5, b = 1
(c) a = -1, b = 5
(d) a = 5, b =​

Answer 1

2x+3y=7

(a+b)x+(2a-b)y=21

(2/a+b) =(3/2a-b)=(7/21)

As (2/a+b) = (3/2a-b)----1⃣

By equation 1⃣

4a-2b = 3a+3b

a=5b-------2⃣

(3/2a-b) =(7/21) ----3⃣

By equation3⃣

63=14a-7b

putting equation 2⃣ in equation 3⃣

63=70b-7b

63=63b

b=1------4⃣

putting equation 4⃣ in equation 2⃣

a=5

So option b is correct ✔

Hope it helps you

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