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Solving System of Equations that have 0, 1, and Infinite Solutions One Solution Solve the following system of equation algebraically and graphically: Both equations equal y. Set them equal to each other. 2 x 22 3x 28 22 5x 28 50 5x 10 x y 2 x 22 y 3x 28 10, 2 y 3 10 28 30 28 2 The lines only intersect once since there is one solution. No Solution Solve the following system of equation algebraically and graphically: 2 x 2 y 18 Add the equations to eliminate a variable: 2 x 2 y 6 2 x 2 y 18 2 x 2 y 6 _____________ 0 12 No Solution. The two lines are parallel. They never intersect. Infinite Solutions Solve the following system of equation algebraically and graphically: The two equations are y 2 x 5 2 y 4 x 10 equivalent. They lie on top of each other. They intersect everywhere. 2 2 x 5 4 x 10 4 x 10 4 x 10 10 10 True Infinite Solutions. Every point that satisfies: y 2 x 5 THE LINES COINCIDE