Q: A chemist is mixing two solutions, one with 20% salt and one with 50% salt, to make 10 liters of a 30% salt solution. Which system of equations represents this scenario?

$$\begin{cases} x + y = 10 \\ 0.2x + 0.5y = 3 \end{cases}$$

Question 1

Given the system of equations $$x + 2y = 10$$ and $$2x - y = 0$$, and the graph shown in the first image, how many solutions does this system have?

Accepted Answer

One solution: $$x = 2, y = 4$$

Question 2

Given the system of equations $$x + 2y = 10$$ and $$3x + 6y = 30$$, and the graph shown in the second image, how many solutions does this system have?

Accepted Answer

Infinitely many solutions.

Question 3

Solve the system of equations: $$y = -3x + 4$$ and $$y = 3x - 2. $$What is the solution?

Accepted Answer

$$x = 1, y = 1$$

Question 4

Solve the system of equations: $$4x + 2y = 10$$ and $$x - y = 13. $$What is the solution?

Accepted Answer

$$x = 5, y = -8$$

Question 5

Solve the system of equations: $$y = x + 2$$ and $$x = -3. $$What is the solution?

Accepted Answer

$$x = -3, y = -1$$

Question 6

Solve the system of equations: $$x - y = 3$$ and $$7x - y = -3. $$What is the solution?

Accepted Answer

$$x = -1, y = -4$$

Question 7

Solve the system of equations: $$-7x + 4y = -24$$ and $$4x - 4y = 0. $$What is the solution?

Accepted Answer

$$x = 2, y = 2$$

Question 8

Solve the system of equations: $$8x - 6y = -20$$ and $$-16x + 7y = 30. $$What is the solution?

Accepted Answer

Question 9

A local cinema sells child tickets for $$7.50 and adult tickets for 10.00. If 1$$,200 tickets were sold for a total of $10,875, how many adult tickets were sold?

Accepted Answer

725

Question 10

Which of the following best describes a system of linear equations that has no solution?

Accepted Answer

The lines are parallel and have different y-intercepts.

Question 11

If a system of equations has infinitely many solutions, what must be true about the equations?

Accepted Answer

They represent the same line.

Question 12

Given the system $$2x - 5y = 9$$ and $$-4x + 3y = 3$$, what is the solution?

Accepted Answer

$$x = 3, y = -1$$

Question 13

Which method is generally most efficient for solving a system of equations when one equation is already solved for a variable?

Accepted Answer

Substitution

Question 14

A chemist is mixing two solutions, one with 20% salt and one with 50% salt, to make 10 liters of a 30% salt solution. Which system of equations represents this scenario?

Accepted Answer

$$\begin{cases} x + y = 10 \ 0.2x + 0.5y = 3 \end{cases}$$

Question 15

If the solution to a system of equations is $$(x, y) = (2, 4)$$, which of the following systems could this be a solution for?

Accepted Answer

$$x + 2y = 10$$ and $$2x - y = 0$$

Precalculus Study Guide: Systems of Linear Equations and Applications

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