Q: Jerry's experiment requires him to mix a 50% acid solution with an 80% acid solution to create 200 mL of a 65% acid solution. Which system of equations models this scenario?

$$\ x + y = 200 \ $$ and $$\ 0.5x + 0.8y = 0.65 \times 200 \ $$

Question 1

Which of the following best describes a system of linear equations?

Accepted Answer

A set of two or more equations that are to be solved simultaneously.

Question 2

What is the solution to the system of equations $$\ 2x + 3y = 13 \ $$ and $$\ 4x - 3y = 17 \ $$ using the elimination method?

Accepted Answer

$$(5,1.5)$$

Question 3

If two lines are parallel when graphed, what can be said about the system of equations?

Accepted Answer

The system has no solution.

Question 4

Given the system $$\ y = 2x + 1 \ $$ and $$\ y = -x + 4 \ $$, what is the solution to the system?

Accepted Answer

$$(1,3)$$

Question 5

Which method is most useful when one of the equations in a system has an isolated variable?

Accepted Answer

Substitution method

Question 6

A restaurant ordered three hampers of blue crabs and one hamper of shrimp that together weighed 80 pounds. In another order, two hampers of shrimp and five hampers of blue crabs weighed 180 pounds. Which system of equations represents this scenario?

Accepted Answer

$$\ 3x + y = 80 \ $$ and $$\ 5x + 2y = 180 \ $$

Question 7

What is the slope and y-intercept of the equation $$\ 5x + 3y = 15 \ $$?

Accepted Answer

Slope: $$\ -5/3 \ $$, y-intercept: $$\ 5 \ $$

Question 8

If a system of equations has infinitely many solutions, what does the graph of the system look like?

Accepted Answer

The lines coincide (are the same line).

Question 9

Solve the system using substitution: $$\ x + 2y = 4 \ $$ and $$\ -2x + 8y = 4 \ .$$

Accepted Answer

$$(0,0.5)$$

Question 10

Which of the following is a dependent system?

Accepted Answer

$$\ 2x + 4y = 8 \ $$ and $$\ x + 2y = 4 \ $$

Question 11

A system of equations is said to be inconsistent if:

Accepted Answer

It has no solution.

Question 12

Which of the following is the correct first step in the elimination method for solving $$\ 2x + 3y = 6 \ $$ and $$\ 3x + 5y = 8 \ $$?

Accepted Answer

Multiply the first equation by 3 and the second by 2.

Question 13

A lacrosse field has a perimeter of 340 yd. The length is 10 yd less than twice the width. Which system of equations models this scenario?

Accepted Answer

$$\ 2L + 2W = 340 \ $$ and $$\ L = 2W - 10 \ $$

Question 14

Which of the following is NOT a possible outcome when graphing a system of two linear equations?

Accepted Answer

The lines form a circle.

Question 15

During the summer months, the Bronx Zoo charges $$11 for adults and 8 $$for children and seniors. One busy day, a total of $4700 was collected from 500 visitors. Which system of equations represents this scenario?

Accepted Answer

$$\ x + y = 500 \ $$ and $$\ 11x + 8y = 4700 \ $$

Question 16

What is the solution to the system $$\ 3x + 2y = 1 \ $$ and $$\ x = y - 8 \ $$ using substitution?

Accepted Answer

$$(5,13)$$

Question 17

If a system of equations is independent, what does this mean?

Accepted Answer

The equations are not multiples of each other and have exactly one solution.

Question 18

Jerry's experiment requires him to mix a 50% acid solution with an 80% acid solution to create 200 mL of a 65% acid solution. Which system of equations models this scenario?

Accepted Answer

$$\ x + y = 200 \ $$ and $$\ 0.5x + 0.8y = 0.65 	imes 200 \ $$

Question 19

Which of the following is the correct solution to the system $$\ 2x - 6y = 8 \ $$ and $$\ 4x - 12y = 16 \ $$?

Accepted Answer

Infinitely many solutions

Systems of Linear Equations: Graphing, Substitution, Elimination, and Applications

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