1. which graph shows the system of inequalities? $2x + y \geq 3$ $y \geq -2x - 3$ (a) graph a (b) graph b (c) graph c 2. the system of equations models the price per share, $y$, for two stocks over time, $x$. which represents the viable solutions to the system? $-y \leq 3x + 4$ $-3x + 3y \leq -9$ (a) all real number values of $x$ and $y$ (b) $(5, 15)$ (c) all real number values, with $y \geq 0$ (d) $(15, 5)$ 3. kona wants to bake at most 30 loaves of banana bread and nut bread for a bake sale. each loaf of banana bread, $x$, sells for $2.50, and each loaf of nut bread, $y$, sells for $2.75. kona wants to make at least $44. which system of inequalities models the situation? (a) $x + y 44$ (d) $x + y \geq 30$; $2.5x + 2.75y \geq 44$ 4. which is the graph of the system of inequalities in item 3? (a) graph a (b) graph b (c) graph c (d) graph d 5. cian is buying movie tickets for a group. he wants to have at least 30 tickets and spend no more than $400. adult tickets cost $12.50 and child tickets cost $7.50. which system of inequalities can be used to find the number of each type of ticket cian could buy? (a) $x + y \geq 30$; $7.5x + 12.5y \leq 400$ (b) $x + y \leq 30$; $7.5x + 12.5y \geq 400$ (c) $x + y \geq 30$; $7.5x + 12.5y \geq 400$ (d) $x + y \leq 30$; $7.5x + 12.5y \leq 400$ algebra 1 • assessment resources

Question

1. which graph shows the system of inequalities? $2x + y \geq 3$ $y \geq -2x - 3$ (a) graph a (b) graph b (c) graph c 2. the system of equations models the price per share, $y$, for two stocks over time, $x$. which represents the viable solutions to the system? $-y \leq 3x + 4$ $-3x + 3y \leq -9$ (a) all real number values of $x$ and $y$ (b) $(5, 15)$ (c) all real number values, with $y \geq 0$ (d) $(15, 5)$ 3. kona wants to bake at most 30 loaves of banana bread and nut bread for a bake sale. each loaf of banana bread, $x$, sells for $2.50, and each loaf of nut bread, $y$, sells for $2.75. kona wants to make at least $44. which system of inequalities models the situation? (a) $x + y < 30$; $2.5x + 2.75y < 44$ (b) $x + y \leq 30$; $2.5x + 2.75y \geq 44$ (c) $x + y > 30$; $2.5x + 2.75y > 44$ (d) $x + y \geq 30$; $2.5x + 2.75y \geq 44$ 4. which is the graph of the system of inequalities in item 3? (a) graph a (b) graph b (c) graph c (d) graph d 5. cian is buying movie tickets for a group. he wants to have at least 30 tickets and spend no more than $400. adult tickets cost $12.50 and child tickets cost $7.50. which system of inequalities can be used to find the number of each type of ticket cian could buy? (a) $x + y \geq 30$; $7.5x + 12.5y \leq 400$ (b) $x + y \leq 30$; $7.5x + 12.5y \geq 400$ (c) $x + y \geq 30$; $7.5x + 12.5y \geq 400$ (d) $x + y \leq 30$; $7.5x + 12.5y \leq 400$ algebra 1 • assessment resources

Accepted Answer

### Question 1:
# Explanation:
## Step1: Analyze the first inequality $2x + y \geq 3$
Rewrite it in slope - intercept form ($y=mx + b$): $y\geq - 2x+3$. The boundary line is $y = - 2x + 3$, with a slope of $-2$ and a $y$ - intercept of $3$. Since the inequality is $\geq$, the line is solid and we shade above the line.
## Step2: Analyze the second inequality $y\geq - 2x - 3$
The boundary line is $y=-2x - 3$, with a slope of $-2$ and a $y$ - intercept of $-3$. Since the inequality is $\geq$, the line is solid and we shade above the line.
Now, we need to find the graph where the shaded regions for both inequalities overlap. The two lines $y=-2x + 3$ and $y=-2x - 3$ are parallel (same slope). The region that satisfies both $y\geq - 2x+3$ and $y\geq - 2x - 3$ is the region above the line $y=-2x + 3$ (because it is above the line $y=-2x - 3$ as well). Looking at the options, we need to identify the graph with the correct shaded region. (Assuming the graphs are as per typical system of inequalities graphs, the correct graph should be the one where the shaded area is above $y = - 2x+3$)
# Answer: (The correct option among A, B, C based on the above analysis. Since the exact graphs are not fully visible, but following the steps, the correct graph should be the one with the shaded region above $y=-2x + 3$)

### Question 2:
# Explanation:
## Step1: Rewrite the first inequality $-y\leq3x + 4$
Multiply both sides by $- 1$ (and reverse the inequality sign): $y\geq - 3x-4$
## Step2: Rewrite the second inequality $-3x + 3y\leq - 9$
Divide both sides by $3$: $-x + y\leq - 3$, then $y\leq x - 3$
Now, we need to find a solution that satisfies both $y\geq - 3x - 4$ and $y\leq x - 3$
- Option A: All real numbers of $x$ and $y$ is incorrect because there are restrictions from the two inequalities.
- Option B: Check $(5,15)$: For $y\geq - 3x-4$, substitute $x = 5,y = 15$: $15\geq-3(5)-4=-15 - 4=-19$ (true). For $y\leq x - 3$, substitute $x = 5,y = 15$: $15\leq5 - 3 = 2$ (false). So $(5,15)$ is not a solution.
- Option C: $y\geq0$ is an extra condition not from the given system, so incorrect.
- Option D: Check $(15,5)$: For $y\geq - 3x-4$, substitute $x = 15,y = 5$: $5\geq-3(15)-4=-45 - 4=-49$ (true). For $y\leq x - 3$, substitute $x = 15,y = 5$: $5\leq15 - 3 = 12$ (true). So $(15,5)$ is a solution.
# Answer: D. $(15,5)$

### Question 3:
# Explanation:
## Step1: Analyze the number of loaves
Kona wants to bake at most 30 loaves of banana bread ($x$) and nut bread ($y$). "At most" means $x + y\leq30$
## Step2: Analyze the money made
Each loaf of banana bread sells for $\$2.50$ and nut bread for $\$2.75$. She wants to make at least $\$44$. "At least" means $2.5x+2.75y\geq44$
So the system of inequalities is $\begin{cases}x + y\leq30\2.5x + 2.75y\geq44\end{cases}$
# Answer: B. $x + y\leq30$, $2.5x + 2.75y\geq44$

### Question 4:
# Explanation:
The system of inequalities from question 3 is $x + y\leq30$ (boundary line $x + y=30$, slope $- 1$, $y$ - intercept $30$, shaded below the line) and $2.5x+2.75y\geq44$ (boundary line $2.5x + 2.75y = 44$, we can find the $x$ - intercept by setting $y = 0$: $2.5x=44\Rightarrow x=\frac{44}{2.5}=17.6$ and $y$ - intercept by setting $x = 0$: $2.75y=44\Rightarrow y = 16$, shaded above the line). We need to find the graph that shows the intersection of the region below $x + y = 30$ and above $2.5x+2.75y = 44$
# Answer: (The correct option among A, B, C, D based on the above analysis of the regions)

### Question 5:
# Explanation:
## Step1: Analyze the number of tickets
Cian wants to have at least 30 tickets. Let $x$ be the number of adult tickets and $y$ be the number of child tickets. "At least" means $x + y\geq30$
## Step2: Analyze the cost
Adult tickets cost $\$12.50$ and child tickets cost $\$7.50$. He wants to spend no more than $\$400$. "No more than" means $12.5x+7.5y\leq400$ (Note: There seems to be a typo in the options, it should be $12.5x + 7.5y\leq400$ instead of $7.5x+12.5y$ as adult tickets are $\$12.50$ and child are $\$7.50$. But following the options, if we assume $x$ is child and $y$ is adult, but the problem says adult tickets cost $\$12.50$ and child $\$7.50$. So with $x$ as adult and $y$ as child, the cost inequality is $12.5x + 7.5y\leq400$ and the number of tickets inequality is $x + y\geq30$)
Looking at the options, Option A: $x + y\geq30$, $7.5x + 12.5y\leq400$ (assuming $x$ is child and $y$ is adult) satisfies the conditions.
# Answer: A. $x + y\geq30$, $7.5x + 12.5y\leq400$

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QUESTION IMAGE

Question

Explanation:

Question 1:

Step1: Analyze the first inequality \(2x + y \geq 3\)

Step2: Analyze the second inequality \(y\geq - 2x - 3\)

Step1: Rewrite the first inequality \(-y\leq3x + 4\)

Step2: Rewrite the second inequality \(-3x + 3y\leq - 9\)

Step1: Analyze the number of loaves

Step2: Analyze the money made

Answer:

Question 2: