Download 4.9 systems of quadratics

Entry Task
1. Solve the System
x+7=y
-4x + 2 = y
Visualize all of the possible solutions to
2 lines
1 solution as an
Ordered pair
Infinitely man
solutions—
same line
No solution–
Parallel Lines
Chapter 4-9
Solving Systems of Linear and
Quadratic Equations
Learning Target: I can solve
systems of linear and quadratic
equations using substitution
2x  y  8
Systems of Linear Equations
x  y  10
We had 3 methods to solve them.
Method 1 - Graphing
Solve for y.
y  2 x  8
y  x  10
(6, – 4)
2x  y  8
Systems of Linear Equations
x  y  10
Method 2 - Substitution
y  2 x  8
x x  y  10  10
x  2 x  8  10
3 x  18
x6
y y 2(
2 x ) 8
8
y  12  8
y  4
(6, – 4)
2x  y  8
Systems of Linear Equations
x  y  10
Method 3 - Elimination

2x  y  8
x  y  10
3x  18
x 6
( x )yy10
10
y  4
y  4
(6, – 4)
Visualize all of the possible solutions to
a Line & a Parabola
1 solution as an
Ordered pair
2 solutions
No solution
Solve the System Algebraically
Use Substitution
y  x2 1
( xy2x1
) 1 x  1
y  x 1
x x0
x  x  1  0
x  0 or x  1  0
x  0 or x  1
x0
(0, 1)
2
x 1
(1, 2)
Answer: (0,1) (1,2)
Solve the System Algebraically
Use Substitution
y  x2  2x  2
y  2 x  2
y  2x  2
2
2
( 2 xy 
 2x) x2 x2 x2 2
x2
(2, 2)
0  x  4x  4
0   x  2 x  2
2
0  x2
x2
Answer: (2,2)