Systems of Equations
By Graphing
What is it?
• A system compares to functions and
determines when they intersect (where they
have the same x and y values).
Point of
intersection
3 methods of solving
• Graphing
• Substitution
• Elimination
*Graphing is an estimate. The other two
methods are exact.
Steps
1.
2.
3.
4.
Solve for y in each equation.
Graph them both on the same axes.
Identify the point where they cross.
That point (x,y) is the “solution” to the
system.
Example
𝑦 = 4𝑥 − 1
𝑦+𝑥 =4
You try
1
𝑦 = 𝑥+4
3
1
𝑦 =− 𝑥+2
3
You try again
12𝑋 − 9𝑌 = 27
8𝑋 − 6𝑌 = 18
Sometimes you will have to write the
equation…
The new Six Flags is offering 2 payment plans.
Option 1: $5 entrance fee and $1 per ride.
Option 2: $2 entrance fee and $3 per ride.
Which option would you choose?
What factors should you consider?
Option 1: $5 entrance fee and $1 per ride.
Option 2: $2 entrance fee and $3 per ride.
Y=cost
X=# of rides
𝑦 = 1𝑥 + 5
𝑦 = 3𝑥 + 2
Solution: (1.5 , 7)
If you ride
more than 2
rides, option 1
is better.
You try with a partner!
Find the value of two numbers if their sum is 12
and their difference is 4.
4 and 8
• The difference of two numbers is 3. Their sum
is 13. Find the numbers.
5 and 8
This is a thinker….
• A boat traveled 336 miles downstream and
back. The trip downstream took 12 hours.
The trip back took 14 hours. What is the
speed of the boat in still water? What is the
speed of the current?
Solution
• Let y = boat speed in still water
Let x = speed of the current
then
(y-x) = effective speed upstream
(y+x) = effective speed downstream
• 12(y+x) = 336
• 14(y-x) = 336
• y - x = 24
y + x = 28
Graph
• boat: 26 mph, current: 2 mph
Homework