
Introduction: Systems of Equations
Presentation
•
Mathematics
•
8th - 10th Grade
•
Practice Problem
•
Medium
+3
Standards-aligned
Ashley Griffin
Used 172+ times
FREE Resource
7 Slides • 13 Questions
1
Introduction: Systems of Equations
By Ashley Griffin
2
Multiple Choice
Warm Up!
After converting from standard form to slope-intercept form, what will the following equation look like?
4x+2y=6
y=2x+3
y=−21x−3
y=−2x+3
y=−21x+3
3
Fill in the Blanks
Type answer...
4
More money, more problems
You recently received some birthday money, $130 to be exact. You count the number of bills you have and find that you have 17 bills, all either $10 or $5 bills.
How many of each bill do you have?
Hint: Just try guessing and checking first!
5
Poll
Which do you think is correct?
nine $5 bills and eight $10 bills
eight $5 bills and nine $10 bills
ten $10 bills and seven $5 bills
six $10 bills and eleven $5 bills
6
How does this have to do with math?
Sometimes, in math, we are asked for two answers, like how many $5 bills AND $10 bills. Systems of equations are how we solve these problems.
7
You've lost me...
Systems of equations are two or more equations that have the same variables like:
y=x+1
y=-2x+6
which both have x and y
8
Systems of Equations
Systems of equations are used when we are given two pieces of information and asked for two answers from it, like our first question.
9
Solutions are where two lines intersect on a graph and these are our answers.
The solution here is (-1,3) because that is where the lines intersect!
Solutions=answers
10
Multiple Select
What is a solution to a system of linear equations?
The point where both lines intersect
The point where the y-axis and x-axis meet
An ordered pair that both lines share
A salt dissolved in water
11
Multiple Choice
What would the solution be to this system of linear equations?
(0,-1.5)
(1, -3)
(5,0)
(0,0)
12
Multiple Choice
What would the solution be to this system of linear equations?
(0,0)
(2,2)
(6,0)
(0,4)
13
14
Multiple Choice
When would we get "infinitely many solutions" to a system of equations?
The lines are parallel, never intersecting
The lines cross at one point
The lines are the same and overlap at all points
The lines cross at 2 points
15
Multiple Choice
When will we get "no solutions" from a system of equations?
The two lines cross once
The two lines are the same and overlap
The two lines are parallel and never touch
The two lines cross at 2 points
16
Fill in the Blanks
Type answer...
17
Fill in the Blanks
Type answer...
18
Fill in the Blanks
Type answer...
19
Match
Match the following graphs to the systems of equations
y=32x+1
y=32x−2
y=−x+7 y=2x+1
y=−2x+4 y=−2x+4
20
Multiple Choice
Which of the following graphs would fit the system of equations?
y=2x−4
y=−21x+1
Introduction: Systems of Equations
By Ashley Griffin
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