Question

How many solutions does this system have?
-3x + 6y=10
-3x + 6y=-4
A. none
B. one
C. infinite
D. two

Answer 1

since the left hand sides of the equations are exactly the same, you will always get the same number when you plug in for x and y, so it is impossible for them to equal different numbers.

Answer 2

is it one?

Answer 3

if they cant ever equal different things, and we have them set to equal different things, then there can be no solutions

Answer 4

multiply the first equation by -1

we now have

\(3x-6y=-10\\-3x+6y=-4\)

Now add them together
\(-3x+3x-6y+6y=-14\\0=-14\\\ \\\huge{\text{YIKES!}}\)

Answer 5

multiply the first equation by -1

we now have

\(3x-6y=-10\\-3x+6y=-4\)

Now add them together
\(-3x+3x-6y+6y=-14\\0=-14\\\ \\\huge{\text{YIKES!}}\)