Download Warm – Up 1.8 Graph. y = 3x – 6

Algebra 3
Warm – Up 1.8
Graph.
y = 3x – 6
Algebra 3
Lesson 1.8
Objective: SSBAT solve a system of equation by
graphing.
Standards: M11.D.2.1.4
What does it mean to say the ordered pair (3, 13)
is a solution to the equation y = 2x + 7?
 When you put the 3 in for x and the 13 in for y into
the equation you get a true statement.
13 = 2(3) + 7
13 = 13
Give 1 solution to each equation using its graph.
1.
y = -7x – 5

(-1, 2)
This is only 1 there
are an infinite number
of solutions
2.
x
y 3
2
Any 1 of these is
correct:
(-6, 0)
(-4, 1)
(-2, 2)
(0, 3)
(2, 4)
(4, 5)
(6, 6)
Review: A graph of an equation shows all the
ordered pairs that are Solutions to that equation.
The graphs for the
equations y = 3x-2 and
y= -x – 6 are shown.
 What ordered pair
is a solution to both
equations?
(-1, -5)
Continued:
What does that mean…
 (-1, -5) is a solution to y = 3x – 2 and it is a
solution to y = -x – 6
-5 = 3(-1) – 2
-5 = -(-1) – 6
-5 = -3 – 2
-5 = 1 – 6
-5 = -5
-5 = -5
Checks.
Checks.
System of Equations
 A set of 2 or more equations that use the
same variables.
 We use a brace to keep the equations
together. Example:
y  x  3

 y  2 x  3
 Linear System – All equations are linear equations.
Solution of a System of Equations
 An ordered pair(s) that makes ALL of the
equations true
(It is a solution to all of the equations)
Solving a System of Equations through Graphing
1. Graph both equations on the same axes
2. The point(s) where the graphs intersect is the
solution.
You want to draw your lines as accurate as possible
 use a ruler
Examples: Solve each System of Equations by Graphing.
1.
 y  x 1

y  x  3
1st: Graph each on the same coordinate plane
 y  x 1
Continued: 
y  x  3
2nd: Find the point of intersection.
(1, -2)
This is the solution to the system of equations –
it is a point on BOTH graphs.
To Check:
Put the solution point into both equations
and see if it works.
 y  x 1

y  x  3
(1, -2)
-2 = -1 – 1
-2 = 1 – 3
-2 = -2
-2 = -2
Yes.
Yes.
It has to work for both to be correct.
y  2 x  8

2. 
y  x  2
The solution is (2, 4)
Solving a Systems of Equations on Graphing Calculator
1. Go to y=
(top left of your calculator)
2. Enter one equation into y1
3. Enter the other equation into y2
4. Hit GRAPH (top right of your calculator
5. Hit 2nd, TRACE (beside the graph key)
6. Choose the INTERSECT option
7. When you get back to the screen with the graphs, hit
ENTER 3 times
3.
 y 1  2x

2 x  y  5
Solve for y first
y = 2x – 1
y = -2x + 5
Solution:
(1.5, 2)
4.
6 x  2 y  12

y  3
 y = -3x + 6
 y=3
is a horizontal line through 3
Solution is (1, 3)
5.
 y  2  3x

 8 y  x  40
 y = 3x – 2
1
y=− 𝑥+5
8
Solution is (2.24, 4.72)
6.
 y  9x  5

 y  9x  7
No Solution  These are parallel lines, which do
not intersect. Therefore there is
no shared ordered pair so there
is no solution to the system of
equations.
7.
Which ordered pair(s) are a solution to the system
of equations below?
(0, -6), (3, 11), (2, 6), (4, 2)
 y  5x  4

2 x  y  10
Answer: (2, 6)
On Own:
8.
x  y  3

 y  3x  1
Solution: (1, 2)
Homework
Worksheet 1.8