PART 1 : LECTURE
SOLVING BY GRAPHING (3.1)
example1:
Consider the system:
(1) y = 3x - 2
(2) y = -1/2 x + 5
You
can solve this system graphically. Each equation has a graph and we are
looking for the intersection between the graph. You need to find the
point (x,y) thay will make both statements true.
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If 2 lines crosses in one point, there is one solution. The system is said consistent.
If 2 lines are parallel, there is no intersection, there is no solution. The system is said to be inconsistent.
If the 2 lines overlaps there is an infinity of solutions. the system is said dependent and consistent.
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example2: solve graphically
(1) 4x - 2y = 10
(2) - 2x + y = -1
Use the slope-intercept form.
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SOLVING BY SUBSTITUTION (3.2)
example3: susbtitution method
(1) - 3x + y = -2
(2) x + 2y = 10
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example4: substitution method
(1) 2x - 3y = -7
(2) 3x + y = -5
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example5: susbstitution method
(1) - 4x + y = 4
(2) 8x - 2y = -8
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PART II: ON YOUR OWN
from book p.245
1) solve this system graphically
y - x = 1
y + x = 3
2) solve graphically
-3x +5 = y
-3x -2 = y
3) solve graphically
3x - 2y = 6
- 12x + 8x = -24
from the book p.253
4) solve by substitution
x+y = 4
x = y+ 1
5) solve by substitution
2x + y = 6
3x + 4y = 4
6) solve by substitution
y = -3x + 5
y = -3x -2
PART III - QUIZ
from assignments due today
PART IV assignments
p. 250 1, 4, 5, 12, 14, 16, 20, 22, 23, 25, 30, 32
p. 257 5, 8, 11, 12, 16, 18, 17
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