a) SUBSTITUTION:

Since y = -2x-1, we can substitute -2x-1 for y in the first equation.

2x + (-2x-1) = 30

2x-2x-1=30

-1=30

Since -1 is NOT equal to 30, then there is no solution to the given system of equations. This means that there is no value for x and y that will make both equations simultaneously true.

b) ELIMINATION

We can multiply both sides of the equation y=-2x-1 by -1. We get -y =2x+1.

Then we add the two equations (actually, add the two left sides and the two right sides).

(2x+y) + (-y) = 30 + (2x + 1)

2x + y – y = 30 + 2x + 1

2x = 31 + 2x

2x-2x = 31

0 = 31

Again, since 0 is NOT equal to 31, we come up with the same conclusion that there is no solution to the system of equations.