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Solving Using Substitution Solve by substitution. Fill in the blanks. { y = -2x + 1 y = 4x - 5 = 4x - 5 ( , ) Solve the system. { y = 4x + 2 y = 10 Answer: ( , ) Is (-4, -1) a solution of { 3x - 2y = -10 5x - 11y = -9 ? yes no Solve the system. { 2x - y = 2 y = 10 Answer: ( , ) Solve the system. { 4x -2y = 10 x = 4 Answer: ( , ) Solve the system. { y = -5x + 1 5x + 2y = 7 Answer: ( , ) (This means they are parallel lines!) When our variables disappear and we are left with a false statement, the answer is "no solution". (This means they are completely overlapping!) When our variables disappear and we are left with a true statement, the answer is "infinitely many". Infinitely many 4x - 2y = 4 y = 2x - 2 4x - 2(2x - 2) = 4 4x - 4x + 4 = 4 4 = 4 Solve the system. { 4x -2y = 10 y =2x +5 Infinitely many No solution Solve the system. { 3x+ y = 6 y = -3x + 6 Infinitely many No solution |