Question

solve the following pair of linear equations for x and y using elimination method. 2a-3/b=12; 5a-7/b=1 ​

Answer 1

Answer:

a = -81, b = -1/58

Step-by-step explanation:

let 1/b = x;

then equation becomes:

5a - 7x = 1 => 10a - 14x = 2...(1)

2a - 3x = 12 => 10a - 15x = 60...(2)

subtracting 1 from 2:

-15x + 14x = 60 - 2

-x = 58

x  = -58            (b = 1/x = -1/58)

replacing x in 2a - 3x = 12

2a + 174 = 12

2a = -162

a = -81

hope it helps :)

Answer 2

Step 01: Renaming equations

The given equations are:

2a – 3/b = 12 …………… (i)

5a – 7/b = 1 …………… (ii)

Step 02: Multiplication (if required)

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)

Step 03: Subtraction of equations

Subtracting (v) and (vi), we get

Subtracting

In attachment!!

or, c = 58 /-29

or, c = -2

But 1/b = c

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

Step 04: Putting the value of variable,we just found in another equation.

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.

$\huge\mathbb{\purple{DORAEMONxNOBITA}}$