Question

Which system of equations has no solutions

A. 3x + 4y = 5
6x + 8y = 10

B. 7x - 2y = 9
7x - 2y = 13

C. 2x - y = -11
-2x + y = 11

D. 3x + 6y = 1
x + y = 0

Answer 1

testing them out:
a: multiply by -2 to first equation
-6x -8y = -10
when you add the next equation, they cancel out. we can already tell there is no solution.

b. multiply by -1
-7x + 2y = -9
when you add, both variables subtract, so there is no solution.

c. there is no need to multiply. however, when you go to subtract, you see that the variables subtract out so there is no solution.

d. multiply bottom equation by -3
-3x - 3y = 0
subtract
that leaves 3y = 1
y = 1/3

so, a, b, and c have no solution