# How many solutions does the pair of equations has

#### pksin

How many solutions does the pair of equations x + 2y + 5 = 0 and ?3x – 6y + 1 = 0 have?

#### MarkFL

Multiply the first equation by -3 to obtain:

$$\displaystyle -3x-6y=15$$

yet the second equation implies:

$$\displaystyle -3x-6y=-1$$

so, there is no solution.

This is an inconsistent system; the two lines are parallel, yet separate, so they will not intersect.