Question

Check whether the following pair of equations is consistent or not. If consistent, solve graphically:

x + 3y = 6

3y − 2x = −12 

Answer 1

The given system of equations:

x + 3y = 6

3y − 2x = −12 

To check consistency, we compare the ratios: 

`1/-2 ≠ 3/3`

Since the ratios are not equal, the system of equations is consistent and has a unique solution. 

Rearranging equation (1): 

y = `(6 - x)/3`

Rearranging equation (2): 

y = `(2x - 12)/3`

Setting both equal: 

`(6 - x)/3 = (2x - 12)/3`

Multiplying both sides by (3):

6 − x = 2x − 12

6 + 12 = 2x + x

18 = 3x

x = 6

Substituting x = 6 in equation (1):

6 + 3y = 6

3y = 0

y = 0

The system of equations is consistent, and the solution is (6, 0).

Graphical representation: