# 2.4.ppt.graph.substitution

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```CCGPS Coordinate Algebra
(2-4-13)
UNIT QUESTION: How do I justify
and solve the solution to a system of
equations or inequalities?
Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12
Today’s Question:
When is it better to use substitution
than elimination for solving systems?
Standard: MCC9-12.A.REI.6


1.
2.
3.
Make sure each equation is in
slope-intercept form: y = mx + b.
Graph each equation on the
same graph paper.
The point where the lines intersect
is the solution. If they don’t intersect then
there’s no solution.
4.
Check your solution algebraically.
y = 3x – 12
y = -2x + 3
Solution:
(3, -3)
2 x  2 y  8
2 x  2y  4
Solution:
(-1, 3)
y  2 x  5
y  2 x  1
No
Solution
x  y  2
2 x  3 y  9
Solution:
(-3, 1)
y5
2x  y  1
Solution:
(-2, 5)

There are 3 different types of systems of linear equations
3 Different Systems:
1)
Consistent-independent
2)
Inconsistent
3)
Consistent-dependent
A
system of linear equations having exactly one
solution is described as being consistentindependent. y
 The system has
exactly one solution at
x the point of intersection
A
system of linear equations having no solutions is
described as being inconsistent.
y
 The system has no
solution, the lines are
x parallel
Remember, parallel
lines have the same
slope
A
system of linear equations having an infinite
number of solutions is described as being
consistent-dependent.
y
 The system has
infinite solutions, the
x lines are identical
 If
the lines have the same y-intercept b, and the
same slope m, then the system is consistentdependent
 If
the lines have the same slope m, but different yintercepts b, the system is inconsistent
 If
the lines have different slopes m, the system is
consistent-independent


1.
2.
3.
4.
5.
One equation will have either x or y by itself, or can
be solved for x or y easily.
Substitute the expression from Step 1 into the other
equation and solve for the other variable.
Substitute the value from Step 2 into the equation
from Step 1 and solve.
Your solution is the ordered pair formed by x &amp; y.
Check the solution in each of the original equations.
1. y  6 x  11
 2 x  3y  7
2. 2 x  3 y  1
y  x 1
3. y  3 x  5
5 x  4y  3
4.  3 x  3y  3
y  5 x  17
5. y  2
4 x  3y  18
6. y  5 x  7
 3 x  2 y  12


Graphing and Substitution WS
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