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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