Solve the system. x+y=3 2x+2y=6 (4,-1) (-3,-1) (-2,-1) (1,2) (2,1) (-2,-2) No solution (-1,-2) Infinitely many solutions (3,0) Explain your choice of method.

To solve the system of equations, we can use the elimination method.<br /><br />Given the system of equations:<br />$x+y=3$<br />$2x+2y=6$<br /><br />Step 1: Multiply the first equation by 2 to make the coefficients of $x$ in both equations equal.<br />$2x+2y=6$<br />$2x+2y=6$<br /><br />Step 2: Subtract the second equation from the first equation to eliminate $x$.<br />$(2x+2y)-(2x+2y)=6-6$<br />$0=0$<br /><br />Since the resulting equation is true for all values of $x$ and $y$, it means that the two equations are dependent and represent the same line. Therefore, there are infinitely many solutions to the system of equations.<br /><br />The correct choice is "Infinitely many solutions."