How many solutions does the pair of equations has

Nov 2012
2
0
How many solutions does the pair of equations x + 2y + 5 = 0 and ?3x – 6y + 1 = 0 have?
 
Jul 2010
12,211
522
St. Augustine, FL., U.S.A.'s oldest city
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.