Solving Systems of Equations
Presentation
•
Mathematics
•
9th Grade
•
Medium
+6
Standards-aligned
Shannon Simon
Used 164+ times
FREE Resource
6 Slides • 17 Questions
1
Solving Systems of Equations
2
Methods We Have Used to Solve Systems of Equations
Graphing
Elimination
Substitution
3
Graphing Method
Use the Desmos Graphing Calculator
One Solution: Intersection of the two lines
No Solution: Parallel lines, lines with the same slopes
Infinitely Many Solutions: One line (Both of the lines are the same)
4
Multiple Choice
y = 2x -11
-3y = -6x -15
5
Multiple Choice
y = 7x + 9
2y + 2x = -18
6
Multiple Choice
7
Multiple Choice
8
Multiple Choice
9
Multiple Choice
10
Elimination
Best when the equation is in Standard Form
Look for matching coefficients and variables that OPPOSITE signs
If needed you can multiply by a constant to make variables match and be opposite
11
Substitution
Used when we we have a single variable isolated.
The coefficient of the isolated variable should be 1.
Replace the variable in 1 equation, with the isolated variable from the other equation.
Find the other solution by replacing the unknown variable with the newly found variable.
12
Multiple Choice
What is the best method to use?
2x − 3y = −1
y =x − 1
Graphing
Substitution because a variable is defined
Elimination because the equations are in standard form.
13
Multiple Choice
What is the best method to use?
−4x − 2y = −12
4x + 8y = −24
Graphing
Substitution because a variable is defined
Elimination because the equations are in standard form.
14
Multiple Choice
What variable do you eliminate?
4x + 8y = 20
−4x + 2y = −30
X because they have opposite signs
Y because they have opposite signs
15
Multiple Choice
What is the proper way to set up the equation to begin solving for x?
y = 6x − 11
−2x − 3y = −7
-2(-11) -3y= -7
-2(6x-11) -3y = -7
-2x -3(11) = -7
-2x - 3(6x-11)= -7
16
Multiple Choice
What is the best method to use?
−4x − 2y = −12
4x + 8y = −24
Graphing
Substitution because a variable is defined
Elimination because the equations are in standard form.
17
Multiple Choice
Which variable do you eliminate and why?
7x + 2y = 24
8x + 2y = 30
You pick x because it's LCM is 56
You pick y because it's LCM is 2.
18
Multiple Choice
What variable do you eliminate, and what do you multiply the equation(s) by?
5x + y = 9
10x − 7y = −18
You eliminate x, and multiply the top equation by -2
You eliminate y, and multiply the top equation by 7
19
Multiple Choice
What is the best method do you use?
y = 6x − 11
−2x − 3y = −7
Graphing
Substitution because a variable is defined
Elimination because both equations are in standard form.
20
Writing Systems of Equations
Identify the variables
Look for slopes and starting (y-intercepts)
Write the equation
Solve with Desmos
21
Multiple Choice
y = 8.40 + x
y = 8.40x + 58
y = 8.40x
y = 8.40x - 58
22
Multiple Choice
y=7.30+.90x
x + y = 7.30
y = 7.30 + .65x
y + .65x = 7.30
23
Multiple Choice
Solving Systems of Equations
Show answer
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