Question

Consider the system of linear equations.

y = 34
x + 12

y = 43
x

Part A
How many solutions does the system have?
no solution
exactly one solution
exactly two solutions
infinitely many solutions
Part B
How can you tell?
The slopes of the equations are the same so the lines will not intersect.
The slopes of the equations are different so the lines will intersect at one point.
The slopes of the equations are different so the lines will intersect twice.
The slopes of the equations are the same so the lines will both be the same line.

Answer 1

Interpreting the equations as
y = (3/4)x + 12
y = (4/3)x

Part A: exactly one solution.

Part B: The slopes are different (3/4 and 4/3), so the two lines intersect at exactly one point.

(If you want the intersection, solving (3/4)x + 12 = (4/3)x gives x = 144/7, y = 192/7.)