Case 4: Two Solutions Line: y = -2x + 11 Parabola: y = 2x2 - 8x + 11 Graphical Solution: There are two solutions. (0, 11) is in both tables, so it is one solution. The other point (3, 5) is in the parabola table, and a quick check shows that it's in the line's table. Solutions (0, 11) and (3, 5) Algebraic Solution: y = -2x + 11 y = 2x2 - 8x + 11 Use Comparison: 2x2 - 8x + 11 = -2x + 11 2x2 - 6x = 0 Solve by factoring 2x(x - 3) = 0 x = 0  or  x = 3 Substitute each in y = -2x + 11: x = 0:  y = -2(0) + 11 = 11  Solution (0, 11) x = 3:  y = -2(3) + 11 = 5  Solution (3, 5) Intro | No Solution | One Solution (V) | One Solution (T) | Two Solutions Resources Content, HTML, graphics & design by Bill Willis 2024