Transcript 7.1 Solving Linear systems by graphing

7.1 SOLVING LINEAR SYSTEMS BY GRAPHING
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SOLVE A LINEAR EQUATION BY GRAPHING
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MODELING A REAL LIFE PROBLEM USING A LINEAR SYSTEM
WHAT IS A SYSTEM?
Working with 2 equations at one time:
Example:
2x – 3y = 6
X + 5y = -12
WHAT IS A SYSTEM OF EQUATIONS?
 A system of equations is when you have two or
more equations using the same variables.
 The solution to the system is the point that
satisfies ALL of the equations. This point will be an
ordered pair.
INTERSECTING LINES
 The point where the lines
intersect is your solution.
 The solution of this graph
is (1, 2)
(1,2)
How to Use Graphs to Solve Linear
Systems
y
Consider the following system:
x – y = –1
x + 2y = 5
We must ALWAYS verify that
your coordinates actually satisfy
both equations.
(1 , 2)
To do this, we substitute the
coordinate (1 , 2) into both
equations.
x – y = –1
(1) – (2) = –1 
x + 2y = 5
(1) + 2(2) =
1+4=5
Since (1 , 2) makes both
equations true, then (1 , 2) is the
solution to the system of linear
equations.
x
SOLVING A SYSTEM OF EQUATIONS BY GRAPHING.
Let's summarize! There are 3 steps to solving a system using a graph.
Step 1: Graph both equations.
Write each equation in a form that is easy to
graph. (Slope and y – intercept or x- and yintercepts.) Be sure to use a ruler and graph
paper!
Step 2: Do the graphs intersect?
This is the solution! LABEL the
solution!
Step 3: Check your solution.
Substitute the x and y values into
both equations to verify the point is a
solution to both equations.
1. FIND THE SOLUTION TO THE FOLLOWING SYSTEM:
2x + y = 4
x-y=2
 Graph both equations. I will graph using x- and y-
intercepts (plug in zeros).
2x + y = 4
(0, 4) and (2, 0)
x–y=2
(0, -2) and (2, 0)
Graph the ordered pairs.
2. GRAPH THE EQUATIONS
2x + y = 4
(0, 4) and (2, 0)
x-y=2
(0, -2) and (2, 0)
Where do the lines intersect?
(2, 0)
3. CHECK YOUR ANSWER!
To check your answer, plug the
point back into both
equations.
2x + y = 4
2(2) + (0) = 4
x-y=2
(2) – (0) = 2
Graphing to Solve a Linear System
Work on Foldable!!!!
Solve the following system by
graphing:
3x + 6y = 15
y
–2x + 3y = –3
Using the slope intercept form of
these equations, we can graph
them carefully on graph paper.
y = - 12 x +
y = 23 x - 1
(3 , 1)
5
2
Start at the y - intercept, then use the slope.
Label the
solution!
Lastly, we need to verify our solution is correct, by substituting (3 , 1).
Since 3(3)+ 6 (1) = 15 and - 2(3)+ 3(1) = - 3 , then our solution is correct!
x
ASSIGNMENT
 Ch 7.1 (pg. 401-402)
# 12-36 EVEN