Systems of Equations

Estimate Solutions by Inspection

Solve of Equations by Graphing

Substitution to Solve System of Equations

Test B

Mrs. Williams
Trivia

100

Consider the system of linear equations.

Part A How many solutions does the system have?
Part B How can you tell?

exactly one solution

The slopes of the equations are different so the lines will intersect at one point.

100

If a system of linear equations has an infinite number of solutions, what do you know about the graph of the system?

Sample answer: The lines are the same line.

100

When using substitution to solve a system of equations, how can you tell when a system has no solution?

A system has no solution when the resulting equation is a false statement.

100

How many solutions does the system of equations have?

no solution

100

What is Mrs. Williams favorite color?

Blue

200

Each equation in a system of linear equations has the same slope. What are the possible solutions the system could have?

The system could have either no solution or infinitely many solutions.

200

Solve the system of equations by graphing.

Then write the solution.

y = 2x - 6

y = -4x + 3

(1.5, −3)

one solution

(submit graph for credit) - Quadrant 4

200

Use substitution to solve the system of equations.

5x + y = -24

x + 3y = -2

x= -5, y = 1

(-5, 1)

one solution

200

Solve the system of equations. How many solutions does the system have?

y = -2x + 8

6x + 3y = 24

Infinitely many solutions

200

What is Mrs. Williams shoe size

size 7

or 9.5 women

300

Suri makes $15 per hour and gets a weekly bonus of $25. Juan makes $14 per hour and gets a weekly bonus of $50. Is it possible for Suri and Juan to make the same amount of wages, y, by working the same number of hours, x, in one week? Explain

Yes; Sample answer: Since the slopes of each equation are different, there is one solution. The system will intersect at one point, 25 hours.

300

Solve the system of equations by graphing. Then write the solution.

-2y = -4x + 8

x + y = 5

(3, 2)

one solution

(submit graph for credit) - Quadrant 1

300

Use substitution to solve the system of equations. How many solutions are there?

1/2x - 1/3y = 5

x = 2/3y + 10

5 = 5;

Sample answer: There are infinitely many solutions since the statement is always true.

300

What is the solution to the system of equations? Explain

16x - 2 - 2y = 0

y = 8x + 4

No solution; Sample answer: −10 = 0 is not a true statement.

300

What does Mrs. Williams love to eat?

Will accept:

chicken

salad

Seafood

400

Which system of equations has no solution?

𝖠 3y = 1 + x 𝖡 4x - 5y = 3 𝖢 5x + 4y = 1 𝖣 y = -3x + 4

y = -2x + 5 -3 = 4x - 5y 4x - 2y = 4 y = -3/4x + 1

400

Solve the system of equations by graphing

4x + 6y = 8
y = -2/3x + 1/3

Sample answer: There is no solution because the lines are parallel.

(submit graph for credit)

400

Use substitution to solve the system of equations

y = 4.5x + 7.5

y = -3.5x - 4.5

x= -1.5, y= 0.75

(-1.5, 0.75)

one solution

400

Nia sells pizzas. Large pizzas cost $8 each, and small pizzas cost $6 each. She sold 12 pizzas for $84. How many of each size pizza did Nia sell?

6 small and 6 large pizzas

400

How many kids does Mrs. Williams have? and How many went to college?

Mrs. Williams have 4 children, and 3 went to college.

500

Which system of equations has infinitely many solutions?

𝖠 3y = -5x + 7 𝖡 3y = x - 4 𝖢 2x + y = 2 𝖣 2y = 3x + 6

3x = -5y - 7 3x - 9y = -12 -4x - 2y = 4 4y = 6x + 12

500

The total cost, c, of belonging to two different gyms for m months is shown on the graph. What is the solution of the system? Explain what it means in the situation.

(4, 250); Sample answer: At 4 months, the cost for each gym is the same, $250.

500

Tickets to a school play cost $3 for students and $8 for adults. On opening night, $1,000 was collected and 150 tickets sold. How many of each kind of ticket were sold? Write a system of equations and use substitution to solve.

Sample answer: s + a = 150 and 3s + 8a = 1,000;

40 student tickets and 110 adult tickets were sold

500

A 40-question test has 132 possible points. There are m 5-point questions and n 1-point questions. How many of each type of question is on the test?

m= 23

n= 17

500

When is Mrs. Williams birthday?

May 7th

****Taurus*****