Question

How do you solve this system of equation: `6x + 5y = 9; 36x + 30y = 8`?

Answer 1

No solution.

Explanation:

The two equations are

`6x+5y=9` .............(1) and

`36x+30y=8` .............(2)

It is observed that the LHS of equation (2) is exactly `6` times that of equation (1), so multiplying (1) by `6` and subtracting (2) from it we get

`6(6x+5y)-(36x+30y)=6xx9-8`

or `36x+30y-36x-30y=46`

or `0=46`

Hence, as we tried to eliminate one variable, not only the other is also eliminated, but we get an equality, which is not true.

This means we do not have a solution to the system of equations.

Graphically, in such cases, when we draw the two lines, the two are parallel, as is seen from te graph of these equations, shown below.

graph{(6x+5y-9)(36x+30y-8)=0 [-4.98, 5.02, -2.24, 2.76]}