# Graphing Systems Notes ```The cost of bowling at bowling alley A
or B is a function of the number of
games g.
Cost A = 2.5g + 2
Cost B = 2g + 4
When are the costs the same?


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
Learning Target:
Students can find the solution to a
system of equations by graphing.
Standard: MCC9-12.A.REI.6
The lines can
intersect
The lines can be
parallel (same
slope)
The lines can
coincide (one on
top of the other)
• A consistent system is a system that has at least
one solution.
• An inconsistent system has no solution.
• An independent system has EXACTLY one
solution.
• A dependent system has infinite solutions.
Consistent
Independent
Inconsistent
Consistent
Dependent

There are 3 different types of systems of linear equations
3 Different Systems:
1)
Consistent-independent
2)
Consistent-dependent
3)
Inconsistent
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. If the lines are the same, there
are infinite solutions)
4.
𝒚 = 𝟑𝒙 − 𝟏𝟐
𝒚 = −𝟐𝒙 + 𝟑
Solution: (3, -3)
2𝑥 − 2𝑦 = −8
2𝑥 + 2𝑦 = 4
Solution: (-1, 3)
𝑦 = −2𝑥 + 5
𝑦 = −2𝑥 + 1
No Solution
2𝑦 = 4𝑥 + 6
−8𝑥 + 4𝑦 = 12
Infinite Solutions
𝑦=5
𝑥 = −2
Solution: (-2, 5)
 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
Guided Practice
1-30.
 Questions

*Even #’s Only*






```