Q: A bookstore sells magazines for $$2.45$$ each and cards for $$3.15$$ each. If a customer spends $$60.55 on$$ $$8$$ magazines and $$y$$ cards, which equation represents this situation?

$$2.45 \times 8 + 3.15y = 60.55$$

Question 1

Solve the simultaneous equations:

$$3x - 8y = 22$$

$$x + 4y = 4$$

What is the value of $$x$$?

Accepted Answer

$$x = 6$$

Question 2

Solve the simultaneous equations:

$$3x - 8y = 22$$

$$x + 4y = 4$$

What is the value of $$y$$?

Accepted Answer

$$y = -0.5$$

Question 3

Esme buys $$x$$ magazines at $$2.45 each and y$ cards at 3.15 $$each. Which expression gives the total cost, in dollars, of the magazines and the cards?

Accepted Answer

$$2.45x + 3.15y$$

Question 4

Esme spends $$60.55 in total. She buys 8 magazines at 2.45 $$each and $$y$$ cards at $3.15 each. How many cards does she buy?

Accepted Answer

$$y = 11$$

Question 5

Solve the simultaneous equations:

$$3x - y = 22$$

$$x + 2y = 5$$

What is the value of $$x$$?

Accepted Answer

$$x = 8$$

Question 6

Solve the simultaneous equations:

$$3x - y = 22$$

$$x + 2y = 5$$

What is the value of $$y$$?

Accepted Answer

$$y = -1$$

Question 7

Solve the simultaneous equations:

$$5x - 2y = 26$$

$$7x + 6y = 10$$

What is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 8

Solve the simultaneous equations:

$$5x - 2y = 26$$

$$7x + 6y = 10$$

What is the value of $$y$$?

Accepted Answer

$$y = -3$$

Question 9

A chemist is mixing two solutions. The first solution contains $$x$$ grams of chemical A and the second contains $$y$$ grams of chemical B. If $$3x - 8y = 22$$ and $$x + 4y = 4$$, how many grams of chemical B are in the second solution?

Accepted Answer

$$-0.5$$ grams

Question 10

A bookstore sells magazines for $$2.45$$ each and cards for $$3.15$$ each. If a customer spends $$60.55 on$$ $$8$$ magazines and $$y$$ cards, which equation represents this situation?

Accepted Answer

$$2.45 	imes 8 + 3.15y = 60.55$$

Question 11

Which of the following is the correct first step to solve the system $$x + 4y = 4$$ and $$3x - 8y = 22 by $$substitution?

Accepted Answer

Solve $$x + 4y = 4$$ for $$x$$

Question 12

A student solves $$3x - y = 22$$ and $$x + 2y = 5$$ and finds $$x = 8$$ and $$y = -1. $$Which method could the student have used?

Accepted Answer

Substitution

Question 13

If $$x + 4y = 4$$, what is $$x in $$terms of $$y$$?

Accepted Answer

$$x = 4 - 4y$$

Question 14

A real-world scenario: A doctor prescribes $$x$$ tablets of medicine A and $$y$$ tablets of medicine B. The total cost is $$2.45x + 3.15y$$ dollars. If the patient pays $$60.55$$ and buys $$8$$ tablets of medicine A, how many tablets of medicine B does the patient buy?

Accepted Answer

$$11$$

Question 15

Which of the following systems of equations could represent the intersection point of two lines on a graph?

Accepted Answer

$$3x - 8y = 22$$ and $$x + 4y = 4$$

Question 16

If $$5x - 2y = 26$$ and $$7x + 6y = 10$$, what is the value of $$7x + 6y$$ when $$x = 2$$ and $$y = -3$$?

Accepted Answer

$$10$$

Question 17

Which of the following best describes the solution to a system of two linear equations in two variables?

Accepted Answer

The point where the two lines intersect

Solving Simultaneous Equations and Applications in College Algebra

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