Question

2a-3/b=12 5a-7/b=1
using elimination method step by step​

Answer 1

Step-by-step explanation:

The given equations are:

2a – 3/b = 12 …………… (i)

5a – 7/b = 1 …………… (ii)

Put 1/b = c, we have

2a – 3c = 12 …………… (iii)

5a – 7c = 1 …………… (iv)

Multiply equation (iii) by 5 and (iv) by 2, we get

10a – 15c = 60 …………… (v)

10a + 14c = 2 …………… (vi)

Subtracting (v) and (vi), we get

$10a - 15c = 60 \\ 10a + 14c = 2 \\ = ======= \\ \: \: \: \: \: \: - 29c = 58$

or, c = 58 /-29

or, c = -2

But 1/b = c

Therefore, 1/b = -2 or b = -1/2

Subtracting the value of c in equation (v), we get

10a – 15 × (-2) = 60

or, 10a + 30 = 60

or, 10a + 30 - 30= 60 - 30

or, 10a = 60 – 30

or, a = 30/10

or, a = 3

Therefore, a = 3 and b = 1/2 is the solution of the given system of equations.