2. how many solutions does this system have? 2x + y = 3, 6x = 9 – 3y
a) 1
b) none
c) infinite
d) 2

The system of equation has infinite solution.

C is correct.

Step-by-step explanation:

We are given system of equation

2x + y = 3

6x = 9 – 3y

First we re-write the second equation in standard form

So, we add 3y both sides

6x+3y=9 (2)

2x+y = 3  (1)

Multiply equation 1 by 3

3(2x)+3y = 3(3)

6x+3y=9

Subtract new equation from 2nd equation

6x-6x + 3y-3y = 9-9

0=0

LHS=RHS

This is true statement. If statement is true then infinite number of many solution.

Hence, The system of equation has infinite solution.