Graphing
Substitution
Elimination
Word Problems
Inequalities
100
What does the solution to a system of equations represent on a graph?
The point where two lines intersect (cross)
100
When is substitution the best method to use?
When one equation is already solved for a variable. (isolated)
100
What is the goal of the elimination method?
To eliminate one variable by adding or subtracting equations
100
Fill in the blank based on the following word problem:
A pair of shoes and a jacket cost $52 total. The shoes cost $14 more than the jacket. Write a system of equations to find the cost of the shoes x and the cost of the jacket y.
x + y = _____
y=x - ___
blank 1: 52
Blank 2: 14
100
On a graph what does the solution to a system of equations look like?
The place where the two shaded areas overlap
200
Two lines intersect at ( -2 , 5) what is the solution to the system?
( -2, 5)
200
assuming you start with at least one equation isolated, what is your next step in the substitution process?
Substitute the expression for the variable it equals in the other equation.
200
What should you do if there are no opposite pairs (twins)?
Multiply one or both equations so that you have a opposite pair.
200
You get a solution of ( 5, 2)
Let x represent amount of candy packs bought and y represent amount of drinks bought
Interpret the solution in context to the problem
They bought 5 candy packs and 2 drinks
200
Identify all the points that are solutions to the system of inequalities below:
A and B
300
What is the solution to the system of equations graphed below?
No solution they are parallel
300
Solve using substitution
y= 3x
x + y =16
(4, 12)
300
Solve using elimination
x+y=10
x-y=4
(7,3)
300
In word problems when we have an unknown we use what to represent them?
Variable(s)
300
Using desmos:
Is (2, -2) a solution to
y<-x
2x+y>2
Not a solution
400
Using desmos graph the system and identify the solution
y=2x + 1
y= -x +4
(1,3)
400
To solve how would you set up this system of equations using substitution
y=-2x+1
y=x-5
-2x+1=x-5
400
If elimination leads to both variable pairs canceling out, what does that mean?
No solution
400
Create a system of equations based on the problem below:
A photobook costs $30 plus $0.75 per extra page. A soft cover costs $20 plus $1.50 per extra page. Let x represent the number of extra pages and y represent total cost
y=0.75x + 30
y=1.5x + 20
400
What must you do to the inequality symbol when multiplying or dividing by a negative number?
Flip the inequality sign
500
If two equations graph the same exact line, how many solutions does the system have?
Infinitely many solutions.
500
If substitution results in a false statement like 0 = 5, what does that mean?
NO SOLUTION
500
To solve this system of equations using elimination, first you need to...?
9x+12y=12
3x+5y=25
Multiply by a 3 or (-3)
500
.86 cents
500
Using desmos:
How many solutions to the following system of equations
-2x+3y<2
y>\frac{2}{3}x+3
No solution