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How do you solve a system of quadratic and linear equations?

How do you solve a system of quadratic and linear equations?. x 2 +4x-8 =y 3x+5=y. In this lesson you will learn how to solve a system of a quadratic and linear equation by using substitution. A system of equations: a group of two or more equations. x 2 +4x-8 =y 3x+5=y.

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How do you solve a system of quadratic and linear equations?

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  1. How do you solve a system of quadratic and linear equations? x2+4x-8=y 3x+5=y

  2. In this lesson you will learn how to solve a system of a quadratic and linear equation by using substitution.

  3. A system of equations: a group of two or more equations. x2+4x-8=y 3x+5=y A SOLUTION makes both equations true at the same time

  4. Substitution x2+4x-8=y 3x+5=y =y x2+4x-8 =3x+5

  5. Solutions are coordinate pairs. They have an x AND a y value (4,6) (-1,-4)

  6. x2-6x+5=y y-2x=5 Quadratic function Linear function Use the linear function to substitute y-2x=5 y=2x+5 y x2-6x+5= 2x+5 x2-8x=0 Factor x=0, x=8 x(x-8)=0

  7. Remember, we need to find values for x and y. x2-6x+5=y y-2x=5 We found that x=8, or x=0 y-2(8)=5 y-2(0)=5 y=5 y-0=5 y=21 y-16=5 (0,5) is one solution (8,21) is one solution

  8. 40 30 20 10 - 5 5 10 - 10 Graphs have two intersection points

  9. In this lesson you will learn how to solve a system of a quadratic and linear equation by using substitution.

  10. Solve the system of equations by using substitution. y=3x-30 x2+y2=100

  11. Write two functions (one quadratic and one linear) that as a system will have two real solutions.

  12. Give a system of equations involving a line and a circle that will have two real solutions.

  13. If you needed to solve a quadratic equation which methods would you use, and why? • Graphing? • Taking a square root? • Inspection? • Factoring? • Completing the square? • Quadratic formula?

  14. How many times will a parabola and line cross if the system of equations has two real number solutions? What is the solution to the system of equations? y=x2+1 y-x=1

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