Page 776 - Algebra 1

L E S S O N Graphing and Solving Systems of Linear
112
and Quadratic Equations
Warm Up
1. Vocabulary A set of linear equations with the same variables is called
(55)
a of linear equations.
2. Write 2x2 = -x + 8 in standard form.
(84)
3. Solve 5x - y = 4 + 9x for y. (29)
4. Evaluate 50 - 2x2 for x = -5.
(9) x-y=7
5. Multiple Choice Which ordered pair is a solution of the system 2x + y = -1? (55)
__
A (2,-5) B (6,-1) C (8,-13) D (3,-4)
33
New Concepts
The equations y = 14 - 4x and y = x + 4 are a system of linear equations. The solution (2, 6) is a point at which the graphs of the equations intersect.
A system of equations can also consist of a linear equation and a quadratic equation. The graphs
of three systems each consisting of a quadratic equation, y = x2, and a linear equation are shown.
System A
y = x2 y=x+6
System A has two solutions because the graphs of the system intersect at two points.
System B
y = x2
y = 2x - 1
System B has only one solution.
System C
y = x2
y = 3x - 5
System C has no solution because the graphs do not intersect.
y=
y=x+
x+6
4
16
(-2, 4) 8
y
y=
y
14 -
=
x2
4x
8
x
-4
-2
2
4
y
(3,
9)
x
-4
-2
Math Reasoning
Analyze What are the cordinates of the vertex for every equation of the form y = ax2?
y
2
4
y = x2
16
8
(1, 1)
x
-4
-2
2
4
y = 2x -1
y
16
y=x
2
8
x
Online Connection www.SaxonMathResources.com
-4
-2
y = 3x - 5
2
4
Lesson 112 761