Solving Systems of Equations

Presentation

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Mathematics

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9th Grade

•

Medium

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CCSS

8.EE.C.8B, 8.EE.C.8A, 8.EE.C.8C

Standards-aligned

Shannon Simon

Used 162+ times

FREE Resource

6 Slides • 17 Questions

Solving Systems of Equations

Methods We Have Used to Solve Systems of Equations

Graphing
Elimination
Substitution

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)

Multiple Choice

Solve:
y = 2x -11
-3y = -6x -15

(-1.5,-4)

(1.5,4)

No solution (parallel lines)

Infinitely many solutions

Multiple Choice

Solve:
y = 7x + 9
2y + 2x = -18

(5, 0)

(9, 18)

(-2, -5)

(1, 16)

Multiple Choice

Solve the following system by graphing. What is the solution?

Infinite number of solutions

(3, 3)

(3, -3)

(-3, 3)

Multiple Choice

^{What is the solution?}

-2

(1, 2)

(1, -1)

Multiple Choice

When you graph the exact same equation twice,

you will have no solution.

you will have one solution.

you will have infinite solutions.

you will graph a giraffe.

Multiple Choice

How many solutions will this system have?

No solution

One Solution

I Don't Know

Infinitely Many Solutions

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

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.

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.

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.

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

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

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.

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.

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

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.

Writing Systems of Equations

Identify the variables
Look for slopes and starting (y-intercepts)
Write the equation
Solve with Desmos

Multiple Choice

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

y = 9.65 + x
y = 8.40 + x

y = 9.65x + 43
y = 8.40x + 58

y =9.65x
y = 8.40x

y = 9.65x - 43
y = 8.40x - 58

Multiple Choice

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

y = 6.80 + .65x
y=7.30+.90x

x + y = 6.80
x + y = 7.30

y = 6.80+.90x
y = 7.30 + .65x

y + .90x = 6.80
y + .65x = 7.30

Multiple Choice

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

$10

$15

$20

Solving Systems of Equations

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