Solving Quadratic Systems

1
Solving Quadratic Systems

• Topic 7.7

2
Ways to Solve Systems

• 1. Graphing
• 2. Algebraically
• Substitution
• Elimination can be used, but substitution is
  typically easier

3
Solving by Graphing

• Rewrite each equation for y
• If you take the square root, remember that the
  answers are the expression
• Graph the equations
• On the Casio, Press F5 then F5 again (isect)
• Make sure to choose the two equations that are
  intersecting
• If there is more than one intersection, move the
  direction key to get the others

4
Example Solve the systems of equations
graphically
Answers (0,2) and (4,6)
Answers (5,4) and (2,-4)
5
Solving Algebraically

• Use Substitution
• Solve the easiest equation for one variable
• Plug it into the second equation to get the
  value(s) of one variable
• Plug those value(s) back into the first equation
  to get the value(s) of the other variable

6
Example 1
Rewrite 2nd equation for y
Substitute into 1st equation for y
Solve for x
Plug into 2nd equation
7
Example 2
Rewrite first equation for y2
Substitute y2 in the 2nd equation
Substitute x back in the 1st equation
lt-SAME-gt