Solve the following system of equations by elimination method: 2x + 3

1.	Solve the following system of equations by elimination method: 2x + 3y = 8 4x + 6y = 7
Answer» Given pair of linear equations is 2x + 3y = 8 …(i) And 4x + 6y = 7 …(ii) On multiplying Eq. (i) by 2 to make the coefficients of x equal, we get the equation as 4x + 6y = 16 …(iii) On subtracting Eq. (ii) from Eq. (iii), we get 4x + 6y – 4x – 6y = 16 – 7 ⇒ 0 = 9 Which is a false equation involving no variable. So, the given pair of linear equations has no solution i.e. this pair of linear equations is inconsistent.

Solve the following system of equations by elimination method: 2x + 3y = 8 4x + 6y = 7

Answer»

Given pair of linear equations is

2x + 3y = 8 …(i)

And 4x + 6y = 7 …(ii)

On multiplying Eq. (i) by 2 to make the coefficients of x equal, we get the equation as

4x + 6y = 16 …(iii)

On subtracting Eq. (ii) from Eq. (iii), we get

4x + 6y – 4x – 6y = 16 – 7

⇒ 0 = 9

Which is a false equation involving no variable.

So, the given pair of linear equations has no solution i.e. this pair of linear equations is inconsistent.