Download Solving Systems of Equations by Graphing PowerPoint

Objective: To solve a
system of linear
equations by graphing
and substitution
1. System of Equations - is a set of two or
more equations with the same variables.
2. Solve a System by Graphing - graph the
equations on the same coordinate plane and
find the point of intersection
3. Consistent and Independent –
when a system of equations has
exactly one solution.
4. Consistent and Dependent –
when a system of equations
has infinitely many solutions.
The lines are coinciding.
Classifications of Systems
5. Inconsistent – when a
system of equations has no
solutions. The lines are
parallel.

Graph each system of equations to find their
point of intersection. State the solution.
1. y = 2x – 3
y = -3x +7
These two lines
intersect at the
point (2, 1) which is
the solution to the
system of
equations.
(consistent and
independent)
2. y = x + 5
2x – 2y = -4
-2y = -2x – 4
y=x+2
The two lines are
parallel (they have the
same slope but
different y-intercepts)
so there is NO
SOLUTION.
(inconsistent)
Solve a System by Graphing
Solve problem 3 and 4 by graphing.
3. y = 2x
4. 2x + y = 3
x + y = 12
y = 2x + 3
Solution: (4, 8)
consistent and
independent
Solution: (0, 3)
consistent and
independent

Substitution means to replace one item with
another of equal value.
10. y = -2 + 3(x – 7)
y = 10 – 5x
10 – 5x = -2 + 3(x – 7)
10 – 5x = -2 + 3x - 21
10 – 5x = 3x - 23
-8x = -33
x = 33
8
The second equation tells us that
y is equal in value to 10 – 5x, so
we can substitute 10 – 5x where
we see y in the first equation.
Substitute 33 for x in
8
either equation to find y.
y = 10 – 5(33)
8
y = -85
8
Solution:
 33 85 
 ,

8 
 8
12. y = -1.5x + 7
2y = -3x + 14
The first equation tells us that y is
equal in value to -1.5x + 7, so we
can substitute -1.5x + 7 where we
see y in the second equation.
2(-1.5x + 7) = -3x + 14
-3x + 14 = -3x + 14
14 = 14
14 = 14 is a TRUE
statement so these two
lines would coincide (be the
same line) and we have
INFINITE SOLUTIONS
(consistent and dependent)
NO
Look at the
cost line above the income line
where x = 25 pogo sticks.
YES
About $150
120
That is where the
Costs line and Income line have a common point.
Finish problems 5 – 9 and 11 on the worksheet.