Question

How many solutions does the system of equations have?
y=-2x+9
6x+3y=27

A. one
B. two
C. infinitely many
D. none

Answer 1

To find the number of solutions for the system of equations, we have to solve the system. We can solve this system by substitution or elimination.

Substitution:
From the first equation, we can solve for y:
y = -2x + 9

Substituting this into the second equation:
6x + 3(-2x + 9) = 27
6x - 6x + 27 = 27
27 = 27

The equation simplifies to 27 = 27, which is a true statement.
Since the equation is true, there are infinitely many solutions.

Therefore, the answer is:

C. infinitely many solutions