Transcript October 15, 2009 AIM: How do you solve systems using elimination?

November 2, 2011
At the end of today, you will be able to:
Solve systems of equations using
substitution.
Warm-up:
1. Solve by graphing: y = 2x – 4
y = -x + 5
2. Solve for x:
5x – 4 = 3(x + 1)
3. Solve for x and graph: |2x – 3| > 9
HW 3.2: Pg. 120 #13-18
Quiz Monday!
Check HW 3.1 in back of book
Solving Systems of Equations
• First we learned how to solve by graphing
– Where the lines intersect is the solution! (x,y)
• There are two ways to solve algebraically:
– Substitution Method
– Elimination Method
How does a system of equations work?
Figure out the ages for:
,
if,
,
+
= 16
=5
+
−
=1
Example 1: Solve using Substitution
x + 2y = 8
1
Step 1:
x  y  18
Isolate one of
2
the variables.
Step 2:
Substitute the

value of the
variable in the
2nd equation.
Step 3:

Simplify and
solve for the

variable.
x = 8 – 2y
1
(8  2y)  y  18
2
4  y  y  18
4 – 2y = 18
-4
-4
-2y = 14
y = -7
Wait! You’re
not done,
what does x
equal?
Example 1 continued:
x + 2y = 8
1
x  y  18
2
Step 4: Substitute
again into one of the
equations to solve for
the other variable.

Since y = -7,
x + 2(-7) = 8
x - 14 = 8
+14 +14
x = 22
The solution to the system is x = 22 and y = -7, or
(22, -7)
Practice
Solve using substitution
1. 4c + 2d = 10
c + 3d = 10
2. 4x – 3y = 1
y=x+4
3. y = 4x – 5
y = 8 – 2x