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

To solve the system of equations, we can use the substitution method. <br /><br />Step 1: Solve the first equation for y in terms of x.<br />$y = -x + 3$<br /><br />Step 2: Substitute the expression for y into the second equation.<br />$2x + 2(-x + 3) = 4$<br /><br />Step 3: Simplify the equation.<br />$2x - 2x + 6 = 4$<br />$6 = 4$<br /><br />Since this equation is not true, there is no solution to the system of equations. Therefore, the correct answer is "No solution."