02 Substitution Method.notebook
Graph the System of Linear Equations
x ­ y = 3
3x ­ y = 0
y=x-3
m = 1 (= 1/1)
Line 1
b = -3
y = 3x - 0
mLine
= 3 (=23/1)
b=0
November 25, 2013
The Method of Substitution
Substitution means to replace something with
it's equal.
Cannot read the solution. The lines
cross at aSolution?
point that is not
readable on the graph.
Limitations of Graphing
Steps for using the Method of Substitution
1. Solve ONE of the equations for one of the
variables (whichever equation & variable is
easiest to solve for.)
2. Substitute that variable (the one that you solved for in step 1) in the 2nd equation with what it equals
3. Solve for the remaining variable.
4. Plug answer into equation from
step #1 to find other
variable.
5. Check that your ordered pair works in both original
equations.
Steps
Substitution
Solve using Substitution
Equation 1 is already solved for "y"
Plug in -10 wherever there is a "y"
y = ­10
in the OTHER equation
10x + 2y = 10
10x + 2(-10) = 10
Now, solve for "x"
10(3) + 2y = 10
30 + 2y = 10
-30
-30
2y = -20
2
2
y = -10
10x - 20 = 10
+20 +20
Check that (3, -10)
10x = 30
works
both
LastinStep
10 10
equations.
Now, plug "3" in for
x = 3 "x" and solve for "y"
Example #1
1
02 Substitution Method.notebook
3x ­ y = 7
y = 3x ­ 7
Is an equation already in "x = " or "y = "?
Substitute what "y = " into the top equation
November 25, 2013
2y + x = 3
x = 3
Is an equation already in "x = " or "y = "?
Substitute what "x = " into the top equation
Solve for "y"
Solve for "x"
∞ Solutions
Answer
All Solutions
Answer
(3,
0)
Example #2
y = ­x + 3
2y + 2x = 4
Example #3
Is an equation already in "x = " or "y = "?
Substitute what "y = " into the top equation
Solve for "x"
x ­ y = 10
2x + 3y = 5
Is an equation already in "x = " or "y = "?
Which equation, which variable is easiest to
solve for?
Solve for your remaining variable
False
-∅
Answer
No Solution
Example #4
Answer
(7,
-3)
Example #5
2
02 Substitution Method.notebook
2x + y = 2
4x ­ 2y = ­4
November 25, 2013
Is an equation already in "x = " or "y = "?
Which equation, which variable is easiest to
solve for?
Solve for your remaining variable
Homework:
Worksheet 6-2
Quiz Next Class
Answer
(0,
2)
Example #6
Homework
3