Question

if the system of equations 2x+3y=7 and 2ax+(a+b) y=28 has infinitely many solutions then,

Answer 1

Hey!

_____________

2x + 3y = 7
2ax + (a + b) y = 28

If two equations has infinite solutions, then,

a1 / a2 = b1 / b2 = c1 /c2

2 / 2a = 3 / a+b = -7 / -28

1/a = 3/a+b = 1/4

Now,

1/a = 1/4
a = 4

And

3/a+b = 1/4

12 = 4 + b
12 - 4 = b
b = 8

Thus,

a = 4
b = 8

_____________

Hope it helps...!!!

Answer 2

Answer:

Hey!

_____________

2x + 3y = 7

2ax + (a + b) y = 28

If two equations has infinite solutions, then,

a1 / a2 = b1 / b2 = c1 /c2

2 / 2a = 3 / a+b = -7 / -28

1/a = 3/a+b = 1/4

Now,

1/a = 1/4

a = 4

And

3/a+b = 1/4

12 = 4 + b

12 - 4 = b

b = 8

Thus,

a = 4

b = 8

_____________

Hope it helps...!!!