9­8 Systems of Linear and Quadratic Equations reasonable (adjective) ​
ree zun uh bul Other Word Forms: ​
reasonableness (noun), reasonably (adverb) Definition: ​
Something is reasonable if it makes sense or is sensible. Example: ​
It is reasonable to expect warm weather in Orlando in July. Opposite: ​
illogical, implausible, outrageous, unreasonable A system of linear and quadratic equations may have two solutions, one solution, or no solutions. • If there are two points of intersection, there are two solutions. • If there is one point of intersection, there is one solution. • If there are no points of intersection, there are no solutions. Solve each system by graphing. A.) y = x2 + 4 y = 4x B.) y = x2 + 2x + 1 y = x+1 C.) y = 3x + 4 y = − x2 + 4 In Lesson 6­3, you solved linear systems using elimination. the same technique can be applied to systems of linear and quadratic equations. Solve each system using elimination. D.) y = x2 y = x+2 E.) ​
Sales​
The equations at the right model the numbers y of two portable music players sold x days after both players were introduced. On what day(s) did the company sell the same number of each player? How many players of each type were sold? Substitution is another method you have used to solve linear systems. This method also works with systems of linear and quadratic equations. Solve each system using substitution. F.) y = 3x − 20 y = − x2 + 34 G.) − x2 − x + 19 = y x = y + 80 H.) y = 3x2 + 21x − 5 − 10x + y =− 1 Graphing Calculator​
Solve each system using a graphing calculator. I.) y = − x2 + 2 y = 4 − 0.5x J.) y = − 0.5x2 − 2x + 1 y + 3 =− x K.) − x2 − 8x − 15 = y −x+y = 3