3.1 – Solve Linear Systems by
Graphing
A system of two linear equations in two
variables x and y, also called a linear system,
consists of two equations that can be written
in the following form.
Ax + By = C
Dx + Ey = F
A solution of a system of linear equations in
two variables is an ordered pair that satisfies
each equation.
3.1 – Solve Linear Systems by
Graphing
Example 1:
During one calender year, a state trooper
issued a total of 375 citations for warnings and
speeding tickets. Of these, there were 37
more warnings than speeding tickets. How
many warnings and how many speeding
tickets were issued?
3.1 – Solve Linear Systems by
Graphing
Example 2:
You worked 14 hours last week and earned a
total of $96 before taxes. Your job as a
lifeguard pays $8 per hour, and your job as a
cashier pays $6 per hour. How many hours
did you work at each job?
3.1 – Solve Linear Systems by
Graphing
Example 3:
A gym offers two options for membership
plans. Option A includes an initiation fee of
$121 and costs $1 per day. Option B has no
initiation fee but costs $12 per day. After how
many days will the total costs of the gym
membership plans be equal? How does your
answer change if the daily cost of Option B
increases? Explain!
3.1 – Solve Linear Systems by
Graphing
Example 4:
Graph the linear system and estimate the
solution. Then check the solution
algebraically.
3x + 2y = -4
x + 3y = 1
3.1 – Solve Linear Systems by
Graphing
Example 5:
Graph the linear system and estimate the
solution. Then check the solution
algebraically.
4x – 5y = -10
2x – 7y = 4
3.1 – Solve Linear Systems by
Graphing
A system that has at least one solution is
consistent. If a system has no solution, the
system is inconsistent.
A consistent system that has exactly one
solution is independent and a consistent
system that has infinitely many solutions is
dependent.
3.1 – Solve Linear Systems by
Graphing
3.1 – Solve Linear Systems by
Graphing
Example 6:
Solve the system. Then classify the system as
consistent and independent, consistent and
dependent, or inconsistent.
4x – 3y = 8
8x – 8y = 16
3.1 – Solve Linear Systems by
Graphing
Example 7:
Solve the system. Then classify the system as
consistent and independent, consistent and
dependent, or inconsistent.
2x + y = 4
2x + y = 1