Lesson 10 Taken Out of Context Practice Understanding

Ready

Each of the pairs of equations are equivalent. Determine what operation was performed on each term of the first equation to create the second equation.

1.

$12 x + 4 y = 36$

$3 x + y = 9$

2.

$5 x + 3 y = 7$

$10 x + 6 y = 14$

3.

$6 x + 9 y = 50$

$9 y = - 6 x + 50$

4.

$7 x + 4 y = 56$

$21 x + 12 y = 168$

5.

$8 x + 4 y = 16$

$- 4 x - 2 y = - 8$

6.

$18 x + 9 y = 48$

$- 6 x - 3 y = - 16$

Set

Write each equation in slope-intercept form. Based on the slope-intercept form of the equations, determine whether the system of equations has zero, one, or infinitely many solutions. How do you know?

7.

$3 x - 4 y = 13$ Slope-intercept form:

$y = - 3 x - 7$ Slope-intercept form:

How many solutions?

How do you know?

8.

$3 x - 3 y = 3$ Slope-intercept form:

$x - y = 1$ Slope-intercept form:

How many solutions?

How do you know?

9.

$0.5 x - y = 30$ Slope-intercept form:

$0.5 x - y = - 30$ Slope-intercept form:

How many solutions?

How do you know?

10.

$4 x - 2 y = - 2$ Slope-intercept form:

$3 x + 2 y = - 12$ Slope-intercept form:

How many solutions?

How do you know?

Solve each system. Write your solution as an ordered pair, or indicate if it has no solutions, or infinitely many solutions.

11.

${\begin{cases} x + 4 y = 6 \\ x + y = 3 \end{cases}$

12.

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

13.

${\begin{cases} y = 2 x + 1 \\ 2 x - y + 1 = 0 \end{cases}$

14.

${\begin{cases} 4 y - 5 x = 9 \\ x - 4 y = 11 \end{cases}$

15.

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

16.

${\begin{cases} - 2 x + 5 y = - 1 \\ 3 x + 2 y = 11 \end{cases}$

17.

${\begin{cases} 2 y = x + 2 \\ - \frac{1}{2} x + y = 1 \end{cases}$

18.

${\begin{cases} 2 y = 2 x - 2 \\ - \frac{1}{2} x + \frac{1}{2} y = 1 \end{cases}$

19.

${\begin{cases} - 2 y = 4 x + 2 \\ 8 x - 4 y = - 4 \end{cases}$

Go

Graph the following inequalities. Justify the region you shade by showing at least one point in the region as being a solution to each inequality.

20.

$3 x - 4 y \geq 12$

21.

$x + 6 y < 6$

22.

$6 x + 5 y > 1$

23.

$x - \frac{1}{2} y \geq 3$

24.

a.

On the same set of axes graph, $y < x + 2$ and $y > x + 5.$

b.

Do the solution sets of these two inequalities share any points? Explain.

25.

a.

On the same set of axes graph, $y < x + 2$ and $y < x + 5$ .

b.

Do the solution sets of these two inequalities share any points? Explain.