Transcript Systems of Equations

Math Minutes
•Pick up a study guide as you come in.
•Complete #26-29 only in the Math Minutes packet.
DO NOT GO ON!!!.
•Finished? Work on TCAP Mastery. It’s due
tomorrow! If you would like it checked, have it out
on your desk.
Must show work on both to receive
credit!!!
Most Missed Test Questions
Tamara read a newspaper article about the cost of attending a university in 2005.
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The average cost to attend a public university was about $12,000 per year.
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The average cost to attend a private university was about $30,000 per year.
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The author of the article stated that a person would save between $40,000 and
$50,000 over 4 years by attending a public university.
Which statement best describes the author’s statement?
A. It is valid because the total cost over 4 years of attending both types of universities
is about $42,000.
B. It is invalid because the total cost over 4 years of attending both types of
universities is about $168,000.
C. It is invalid because the difference in costs over 4 years of attending a private
university to a public university is about $18,000.
D. It is invalid because the difference in costs over 4 years of attending a private
university to a public university is about $72,000.
***Most chosen incorrect answer was C***
Most Missed Test Questions
***Most chosen incorrect answer was C***
Why is “C” incorrect?
The diagram below shows the location of two schools on a map. The length of
each grid square represents one mile.
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One route requires traveling northeast on Lookout Road.
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One route requires traveling east on Broadway and north on Main Street.
What is the approximate difference between these routes?
Main
Street = 11
miles
Lookout Road
A. 7.6 miles
B. 11.0 miles
C. 19.4 miles
Broadway = 16 miles
D. 27.0 miles
Mrs. Manley
Systems of
Equations
How do you find solutions to
systems of two linear
equations in 2 variables?
Lesson Objective
❖
Use the substitution method to solve a system of linear
equations
A set of linear equations in two variables is called a system of linear
equations.
3x + 2y = 14
2x + 5y = 3
A solution of such a system is an ordered pair which is a solution of
each equation in the system.
Example: The ordered pair (4, 1) is a solution of the system since
3(4) + 2(1) = 14 and 2(4) – 5(1) = 3.
Example: The ordered pair (0, 7) is not a solution of the system
since
3(0) + 2(7) = 14 but 2(0) – 5(7) = – 35, not 3.
Systems of linear equations in two variables have either no solutions,
one solution, or infinitely many solutions.
y
y
x
unique solution
y
x
infinitely many
solutions
x
no solutions
A system of equations with at least one solution is consistent. A system
with no solutions is inconsistent.
Substitution Method
1. Choose one equation and solve for y (choose the easiest). In other words, change
the equation to slope- intercept form - y = mx + b.
2. Substitute the expression that equals y into the remaining equation for the y
variable.
3. Solve for x.
4. Now, substitute the value found for x back into either of the original equations.
5. Solve for y.
6. Write your solution as a coordinate pair (x,y).
7. Check your solution (x,y) to be sure it works in both the original equations.
Slope-Intercept Form
y = mx + b
y = mx + b
y=x-2
y = -x - 4
Examples
Y = 4x + 3
Y=x
Examples
y = -2x + 10
y=x+1
Examples
y -1/4x + 5
y=x+2
Examples
y=x+1
y = -4x + 10
y = mx + b
ax + by = c
y = 2x - 7
-3x + 6y =12
Examples
3x + 5y = 10
y=x+2
Examples
-2x + y = 6
y = -4x - 12
Examples
3x + 4y = 11
y = 2x
Examples
-4x + 8y = 12
y = -12x + 64
Standard Form
ax + by = c
ax + by =c
3x + y = 2
x - 2y = 10
Examples
-3x + 5y = 10
2x + ½y = 24
Examples
-2x + 1/3y = 7
6x – 1/5y = -9
Examples
7x – 2y = -13
x – 2y = 11
Examples
-4x + y = 6
-5x – y = 21
Example 1
3x + 2y = -1
x-y=3
Example 2
4x + 6y = 12
6x + 9y = 36
Example 3
4x + 5y = 3
2x - 3y = 7
Example 4
2x + y = 3
4x + 2y = 5