Transcript Methods to Solving Systems

Warm Up #
Rewrite the equations in slope-intercept form
(y = mx + b).
1. 2y = 3x + 5
2. y - 5 = 2x - 3
Rewrite the equations in standard form (Ax + By = C).
3. 6y = -4x - 9
4. 5x - 3 = 2y + 8
Is the ordered pair a solution of the equation?
5. y = 3x - 2; (4, 8)
6. x - 7y = -1; (6, 1)
ACT
9. What is the x-intercept of a line that
passes through the point (3, 4) and has
a slope of 2?
F. –2
G. –1
H. 0
J. 1
K. 2
Unit 8 Lesson 1: Solving Systems of Equations
OBJ’S
● I can solve a system of equations graphically, both
by hand and using technology
● I can solve a system of linear equations using
substitution
○ Teachers may choose to review elimination,
but it will not work with mixed systems
Systems of Equations
System of Linear Equations Two or more linear equations with the
same variables.
Solution of a System of Equations A point (x, y) that satisfies both
equations. If the lines are graphed, it is the point where the lines
intersect (cross).
Methods to Solving Systems
Method 1: Graphing
*Make sure both linear equations are in y-int form.
*Graphing – graph both lines on the same coordinate plane
and determine where they intersect – intersection point is
the solution.
Substitute solution into both equations to check.
Method 2: Graphing with calculator
To use calculator – make sure both equations are in y =
form:
1. put into Y1 = and Y2 = ,
2. graph
3. 2nd CALC 5: Intersection
1. Solve the system by
graphing. By Hand!
y = 2x - 1
y=x+1
2. Solve the system by
graphing with calculator
y = -2x + 3
-x + y = - 3
Methods to Solving Systems
Method 3: Substitution
Step 1: Solve one of the equations for one of its variables.
Step 2: Substitute the expression from Step 1 into the other
equation.
Step 3: Solve for the variable.
Step 4: Substitute the value (answer from Step 3) into the
original equation.
Step 5: Solve for the other variable.
Step 6: Write your answer as a point (x, y).
Step 7: Check!!
Solve by substitution
3) y = x - 1
x - 5y = -15
5) 6x - 4y = 16
9x - 6y = 24
4) x = 2y
x - 8y = -5
6) 3x + 4y = 12
6x + 8y = -16
Exit Slip
Solve each system of equations using any method
3. 2 + y + x = 0
1. -20x - 7y = -9
2. y = 2x + 3
x = -4
-10x - 2y = 6
y = -2x + 4
Example 1)
The local amusement park is a popular field trip destination. This year the senior class at
High School A rented and filled 16 vans and 5 buses with 417 students. High School B
rented and filled 10 vans and 8 buses with 480 students. Each van and each bus carried
the same number of students. How many students can a van carry? How many students
can a bus carry?
Example 2)
The school that Lisa goes to is selling tickets to the annual talent show. On the first day of
ticket sales the school sold 3 senior citizen tickets and 5 student tickets for a total of $70.
The school took in $216 on the second day by selling 12 senior citizen tickets and 12
student tickets. What is the price each of one senior citizen ticket and one student ticket?
Example 3
The sum of two numbers is 36. Their difference is 24. Find the two numbers.
Example 4
The owner of a men's clothing store bought six belts and eight hats for $140. A week later, at
the same prices, he bought nine belts and six hats for $132. Find the price of a belt and the
price of a hat.
Example 5
If 5 times the smaller of two numbers is subtracted from twice the larger, the result is 16. If the
larger is increased by 3 times the smaller, the result is 63. Find the numbers.
Example 6
You are selling tickets for a high school play. Student tickets cost $4 and general admission
tickets cost $6. You sell 525 tickets and collect $2,876. How many of each type of ticket did you
sell?
Example 7
There are two phone plans. One plan has $28 one time fee,
and 9 cents a min. The second is 13 cents a min. How many
minutes of use will make the plans cost the same?
Example 8
The following table gives the population (in millions) of Georgia and North
Carolina in 1990 and 2003.
Year
1990
2003
Georgia
6.5
8.7
North Carolina
6.8
8.4
Assume that the population growths are linear. Find when the two states had
equal populations and find that population.
Example 9
If Robert has ten coins all nickels and dimes worth 70 cents,
kind of coin does he have?
how many of each
With your partner....set up and solve all the word
problems on your handout