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Systems of Linear and Quadratic Equations

Systems of Linear and Quadratic Equations. Find their intersections. Focus 5 Learning Goal – (HS.A-CED.A.3, HS.A-REI.C.5, HS.A-REI.C.6, HS.A-REI.D.11, HS.A-REI.D.12) : Students will write, solve and graph linear systems of equations and inequalities. What does it mean to solve a system?.

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Systems of Linear and Quadratic Equations

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  1. Systems of Linear and Quadratic Equations Find their intersections.

  2. Focus 5 Learning Goal –(HS.A-CED.A.3, HS.A-REI.C.5, HS.A-REI.C.6, HS.A-REI.D.11, HS.A-REI.D.12):Students will write, solve and graph linear systems of equations and inequalities.

  3. What does it mean to solve a system? • To solve a system, we find where the graphs intersect. • You know how to solve a system that contains linear equations. • The two lines intersect at ONE point.

  4. How about the intersection of a line with a quadratic equation? • How many points of intersection does a line have with a parabola? The graph of a quadratic equation is a parabola.

  5. To solve the system graphically: • Analyze the graph. • Determine where the line intersects the parabola. • Write down the ordered pairs. Solution: (1, 3) and (6, 13)

  6. Solve these systems: • (-3, 4) and (1, 0) • (-2, -2) and about (2.5, 2.5)

  7. How to solve the system algebraically: • Make both equations into “y =“ format. • Set them equal to each other. • Solve for x. • You should get 2 values for x. • Substitute both values back into EITHER equation and solve for y. • Write your answers as ordered pairs.

  8. Solve this system: y = x2 + 2x and y = 2x + 4 • Substitute each x- value into either equation and solve for y. • y = 2(2) + 4 • y = 8 • y = 2(-2) + 4 • y = 0 • Since both equations are already “y =“, set them equal to each other. • x2 + 2x = 2x + 4 • -2x -2x • x2 = 4 • Square root both sides. • x = 2 and -2 Solution: (2, 8) and (-2, 0)

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