I. SOLVING BY GRAPHING
Solution(s)
*one solution
*infinitely many
solutions
*Lines have the
same slope (m)
and y-intercept (b)
*No solution
*Lines have the
same slope (m)
only
Examples of Graphs
has exactly one
intersection
over lapping lines (coincide)
No intersection
Classifications
Consistent & independent
Consistent & dependent
Inconsistent
EXAMPLES: SOLVE BY GRAPHING
1) y = -2x
y=x+3
2) y = 3x + 2
y = 3x – 3
3)
x+y=6
-2x – 2y = -12
USING YOUR CALCULATOR TO GRAPH:
Hotel A charges $70 per night and a one-time $5 facility fee. Hotel B
charges $65 per night and a $20 one-time facility fee. After how many
nights will the cost of the two hotels be the same?
If you are only staying 2 nights, which would be a better deal?
If you are staying 5 nights, which would be a better deal?
Write equations for both hotels and graph to find the answer.
II. SUBSTITUTION METHOD
Step 1) Solve one equation for one of its variables.
Step 2) Substitute the expression from Step 1 into the other
equation and solve for the other variable.
Step 3) Substitute the value from Step 2 into the equation
from Step 1 and solve.
EXAMPLES TO FOLLOW…..
EXAMPLE 1) Solve the system by substitution: 6x + 3y = 12
3x + y = 5
EXAMPLE 2: Solve the system by substitution: 2x + y = 4
3x – 5y = 6
EXAMPLE 3: Solve the system by substitution: 3x + 6y = 3
x – 2y = 5
III. ELIMINATION METHOD
Step 1) Multiply one or both of the equations by a constant to obtain
coefficients that differ only in sign for one of the variables.
Step 2) Add the equations together and solve for the remaining
variable.
Step 3) Substitute the value obtained in Step 2 into either of the
original equations and solve for the other variable.
EXAMPLES TO FOLLOW….
EXAMPLE 1) Solve the system by elimination: 7x + 2y = -5
3x – 4y = -7
EXAMPLE 2) Solve by elimination method: 2x – 3y = 3
4x – 5y = 9
EXAMPLE 3) Solve by elimination method: 3x – y = 5
6x – 2y = 10
EXAMPLE 4) Solve by elimination method: x – 2y = 5
4x – 8y = -3
WORD PROBLEM: Your school sells short sleeve t-shirts that cost
the school $5 each and are sold for $8 each. Long sleeve t-shirts
cost the school $7 each and are sold for $13 each. The school
spends $2450 on t-shirts and sells all of them for $4325. How
many of each type of t-shirt are sold?
Define variables:
Write equations:
Solve: