Lesson 5 Pampering and Feeding Time Practice Understanding

Ready

Rewrite the given equations so that they are in slope-intercept form. $(y = m x + b)$

1.

$7 x - 14 y = - 56$

2.

$- 8 x - 2 y = 6$

3.

$15 x + 9 y = 45$

Rewrite the given equations so that they are in standard form.

( $A x + B y = C$ , where $A$ , $B$ , and $C$ are integers and $A$ is positive.)

4.

$y = 7 x - 3$

5.

$y = 2 x + 9$

6.

$y = - 4 x - 11$

7.

$y = \frac{1}{2} x + 8$

8.

$y = \frac{3}{5} x - 2$

9.

$y = - \frac{1}{6} x + \frac{2}{3}$

Set

10.

On a final for a creative writing course, Ben was required to write a combination of at least $10$ poems or paragraphs. Ben knew that each poem would take him $30$ minutes to write, while a paragraph would only take $10$ minutes. Ben was given two hours to complete the exam.

a.

Write an inequality to model each constraint.

b.

Graph each inequality on a separate coordinate grid and shade the solution set for each.

Time Graph:

Items Graph:

11.

The school drama department is putting on a production and plans to charge $$ 10$ for an adult ticket and $$ 5$ for a child ticket. They need to make at least $$ 3,000$ each night to cover the costs. The auditorium can hold $400$ people.

a.

Write an inequality to model each constraint.

b.

Graph each inequality on a separate coordinate grid and shade the solution set for each.

Money Graph:

Tickets Graph:

Go

Solve the system of equations using the algebraic method of substitution. Show your work.

12.

${\begin{cases} y = 5 x - 7 \\ y = 4 x - 5 \end{cases}$

13.

${\begin{cases} y = - 3 x + 12 \\ y = 2 x - 8 \end{cases}$

14.

${\begin{cases} y = 6 x - 23 \\ y = - 4 x + 57 \end{cases}$

15.

${\begin{cases} x = y - 1 \\ y = 4 x - 5 \end{cases}$

16.

${\begin{cases} y = 2 x + 1 \\ 4 x + 5 y = 33 \end{cases}$

17.

${\begin{cases} x = 3 y - 1 \\ 2 x + 5 y = 42 \end{cases}$

Students started solving systems of linear equations by substitution and their first step in solving is shown. Write the original systems that the students were given.

18.

$3 x - 11 = 5 x - 7$

19.

$3 (y + 2) - 4 y = 17$

20.

$- 8 x + 2 (- 6 x + 11) = 82$