6. baseball fans can buy tickets for seats in the lower deck or upper deck of the stadium. tickets for the lower deck cost $42 each. ticket prices for the upper deck are 75% of the cost of tickets for the lower deck. write an inequality representing all possible combinations of x, the number of tickets for the lower deck, and y, the number of tickets for the upper deck, that someone can buy for no more than $800.
(5.8 notes)
7. what is the solution for the system of equations?
6y + x = -59
x = -2y + 9
what is the best method to solve this problem?
(5.1-5.5 notes)
8. what value of x makes this equation true?
4(y - 3) + 19 = 8(2y + 3) + 7
(1.3 notes)
9. write a statement that best represents the slope of the line shown on the grid and its relationship to the y - axis?
the slope of the line is _______, the line is _______ to the y - axis
(4.4 notes)
10. graph the following system of equations to find the solution?
2x + y = -4
-3y = 2x + 12

Question

Accepted Answer

### Question 6
# Explanation:
## Step 1: Find upper deck ticket price
Upper deck price is 75% of lower deck. Lower deck is $42, so upper deck price = $ 0.75 \times 42 = 31.5 $ dollars.
## Step 2: Total cost inequality
Total cost for lower deck: $ 42x $, total cost for upper deck: $ 31.5y $. Total cost ≤ $800, so inequality is $ 42x + 31.5y \leq 800 $.
# Answer: $ 42x + 31.5y \leq 800 $

### Question 7 (System of Equations: $ 6y + x = -59 $, $ x = -2y + 9 $)
# Explanation:
## Step 1: Substitute $ x $ into first equation
Substitute $ x = -2y + 9 $ into $ 6y + x = -59 $: $ 6y + (-2y + 9) = -59 $
## Step 2: Simplify and solve for $ y $
Simplify: $ 4y + 9 = -59 $ → $ 4y = -68 $ → $ y = -17 $
## Step 3: Solve for $ x $
Substitute $ y = -17 $ into $ x = -2y + 9 $: $ x = -2(-17) + 9 = 34 + 9 = 43 $
Best method: Substitution (since $ x $ is already solved for in the second equation).
# Answer: Solution is $ x = 43 $, $ y = -17 $; Best method: Substitution.

### Question 8 (Solve $ 4(y - 3) + 19 = 8(2y + 3) + 7 $)
# Explanation:
## Step 1: Expand both sides
Left: $ 4y - 12 + 19 = 4y + 7 $
Right: $ 16y + 24 + 7 = 16y + 31 $
## Step 2: Set equal and solve
$ 4y + 7 = 16y + 31 $ → $ -12y = 24 $ → $ y = -2 $ (Note: The equation has $ y $, not $ x $; maybe a typo, but solving for $ y $)
# Answer: $ y = -2 $ (If solving for $ x $, no $ x $ in equation; likely $ y $ intended)

### Question 9 (Slope and relationship to y - axis)
# Brief Explanations:
The line is horizontal (from the grid, horizontal line). Slope of horizontal line is 0. Horizontal lines are parallel to the y - axis? No, horizontal lines are parallel to the x - axis and perpendicular to the y - axis? Wait, horizontal line: slope is 0, and it is parallel to the x - axis, perpendicular to the y - axis? Wait, no: horizontal line (constant y - value) has slope 0, and is parallel to the x - axis, so perpendicular to the y - axis (since y - axis is vertical). Wait, the grid shows a horizontal line. So slope is 0, and the line is perpendicular to the y - axis? Wait, no: horizontal line is parallel to x - axis, so perpendicular to y - axis (since y - axis is vertical). So slope is 0, and the line is perpendicular to the y - axis? Wait, no, horizontal line and y - axis: y - axis is vertical, horizontal line is horizontal, so they are perpendicular. Wait, no: horizontal line (slope 0) and y - axis (undefined slope, vertical) are perpendicular. So slope is 0, the line is perpendicular to the y - axis? Wait, no, maybe parallel? No, horizontal and vertical are perpendicular. So:
Slope of horizontal line is 0. The line (horizontal) is perpendicular to the y - axis (vertical).
# Answer: The slope of the line is $ 0 $, the line is perpendicular to the y - axis.

### Question 10 (Graph $ 2x + y = -4 $ and $ -3y = 2x + 12 $)
# Explanation:
## Step 1: Rewrite in slope - intercept form ($ y = mx + b $)
First equation: $ y = -2x - 4 $ (slope - 2, y - intercept - 4)
Second equation: $ -3y = 2x + 12 $ → $ y = -\frac{2}{3}x - 4 $ (slope $ -\frac{2}{3} $, y - intercept - 4)
Wait, wait, no: $ -3y = 2x + 12 $ → $ y = -\frac{2x + 12}{3}=-\frac{2}{3}x - 4 $. Wait, but first equation: $ 2x + y = -4 $ → $ y = -2x - 4 $. Wait, different slopes, same y - intercept? Wait, no, let's check again. Wait, maybe I made a mistake. Wait, $ -3y = 2x + 12 $ → divide by - 3: $ y = -\frac{2}{3}x - 4 $. First equation: $ y = -2x - 4 $. So both have y - intercept - 4, different slopes. So they intersect at (0, - 4)? Wait, no, let's solve algebraically. Set $ -2x - 4 = -\frac{2}{3}x - 4 $. Add 4 to both sides: $ -2x = -\frac{2}{3}x $ → $ -2x+\frac{2}{3}x = 0 $ → $ -\frac{4}{3}x = 0 $ → $ x = 0 $, then $ y = -4 $. So solution is (0, - 4).
# Answer: The solution is $ (0, - 4) $ (found by graphing or solving; both lines intersect at (0, - 4)).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 6

Step 1: Find upper deck ticket price

Step 2: Total cost inequality

Step 1: Substitute \( x \) into first equation

Step 2: Simplify and solve for \( y \)

Step 3: Solve for \( x \)

Step 1: Expand both sides

Step 2: Set equal and solve

Answer:

Question 7 (System of Equations: \( 6y + x = -59 \), \( x = -2y + 9 \))