Methods
What are the three methods for solving systems of equations?
Graphing, substitution, elimination
When graphing a system of equations, the solution lies where the lines ______?
intersect
What is the first step to solving a system of equations by substitution?
Ensure at least one equation is in slope-intercept form.
What is the first step when solving a system by elimination?
rearrange so the equations are lined up the same way
At a candy store, Aaliyah bought 3 kilograms of jelly beans and 1 kilogram of gummy worms for $30. Meanwhile, Fred bought 3 kilograms of jelly beans and 3 kilograms of gummy worms for $42. How much does the candy cost?
A kilogram of jelly beans costs $8, and a kilogram of gummy worms costs $6.
Which method would be easiest to solve this system of linear equations?
4x-3y=-2
2x+3y=6
Elimination
What does a system of linear equations with no solution look like on a graph?
parallel lines
Rewrite the following equation in slope-intercept form:
2x - y = 10
y = 2x - 10
What is the last step when solving a system by elimination?
sub your variable into either of the original equations and solve for the remaining variable
Tammy is using ribbon to create girls' hair barrettes. For a craft fair in Princeton, she made 11 small barrettes and 15 large barrettes, using a total of 108 meters of ribbon. Then, for another craft fair in Seaside, she made 11 small barrettes and 12 large barrettes, which used a total of 93 meters. How many yards of ribbon does Tammy use for each?
Tammy uses 3 meters of ribbon on each small barrette and 5 meters on each large one.
Which method tends to be the most reliable?
Graphing
Describe step by step how determine the solution to the following system of equations:
y = 2x+4
y=-x - 2
1. Start with equation 1; plot the y-intercept at positive 4 and use the slope of 2 to go up 2 and over to the right 1.
2. Graph the second equation by plotting the y-intercept at -2 and then going down 1 and right one.
3. See where the lines cross to determine the solution.
Solve this system of equations using substitution:
x+y=-12
-6x+4y=-8
(-4,-8)
When would solving by elimination be easier than solving by substitution?
when the x's or y's are already identical and can be eliminated right away
Mrs. Tang wants to get family portraits taken and is comparing prices between two different photography studios. Pearson Photography charges $6 per portrait sheet, plus $87 for the session fee. Lasting Memories Company charges $77 for the session fee and $8 per portrait sheet. If Mrs. Tang plans to purchase a certain number of portrait sheets, the cost will be the same at either studio. How many portrait sheets would that be? What would the total cost be?
If Mrs. Tang orders 5 portrait sheets, the portrait session will cost $117 at either studio.
Which method would be easiest to solve this system of equations?
y=-2x+3
y=4
Substitution
What does a system of linear equations with infinite solutions look like on a graph?
identical lines, overlapping at every point
Solve this system of equations by substitution:
y=x-2
y=-2/3x+3
(3, 1)
Solve the system of equations using elimination:
3x-6y=3
4x+6y=32
(5, 2)
Mrs. Killion's favorite color.
Purple!
True or false: you will get a different answer if you solve a system with graphing vs. elimination.
False - you should get the same answer
Can a system of linear equations have two solutions? Explain your answer clearly.
No - can't intersect twice!
Solve this system of equations by substitution:
y=-3x
-3x+3y=0
(0, 0)
Solve the system of equations using elimination:
2x+8y=-22
x+5y=-12
(-7, -1)
The number of school days left till summer break (including today!)
11