exam algebra 2 cp 1. solve this system of equations: $ y = -4x + 13 $ $ y = \frac{1}{2}x + 4 $ a. $ (2, -5) $ b. $ (-2, 5) $ c. $ (2, 5) $ 2. what is the correct $ 1^{st} $ step to solve this system of equations? $ 2x + 3y = 9 $ $ 2x - 5y = 3 $ a. add them b. subtract them c. multiply $ 1^{st} $ equation by 5 3. select the coordinate point that is a solution to the following system. $ -4x + 3y = -16 $ $ x - 5y = -13 $ a. $ (4, 7) $ b. $ (7, -7) $ c. $ (7, 4) $ 4. spongebob is a ________. a. sponge b. robert c. moose 5. if you were using substitution to solve the following system, what is the result of the $ 1^{st} $ step? $ y = 4x - 5 $ $ y = 2x + 3 $ a. $ 4x + y = -5 $ b. $ 4x - 5 = 2x + 3 $ c. $ y = 2(4x - 3) - 5 $ 6. the answer to $ 2x + 14 8 + 2x $ is? a. many solutions b. no solution c. $ -6 $ 7. indicate the incorrect step. $ 2x + 4 - x = 19x - 11 $ step 1: $ x + 4 = 19x - 11 $ step 2: $ \div 19x $ $ \div 19x $ a. step 1 b. step 2 c. stepson

Question

exam algebra 2 cp 1. solve this system of equations: $ y = -4x + 13 $ $ y = \frac{1}{2}x + 4 $ a. $ (2, -5) $ b. $ (-2, 5) $ c. $ (2, 5) $ 2. what is the correct $ 1^{st} $ step to solve this system of equations? $ 2x + 3y = 9 $ $ 2x - 5y = 3 $ a. add them b. subtract them c. multiply $ 1^{st} $ equation by 5 3. select the coordinate point that is a solution to the following system. $ -4x + 3y = -16 $ $ x - 5y = -13 $ a. $ (4, 7) $ b. $ (7, -7) $ c. $ (7, 4) $ 4. spongebob is a ________. a. sponge b. robert c. moose 5. if you were using substitution to solve the following system, what is the result of the $ 1^{st} $ step? $ y = 4x - 5 $ $ y = 2x + 3 $ a. $ 4x + y = -5 $ b. $ 4x - 5 = 2x + 3 $ c. $ y = 2(4x - 3) - 5 $ 6. the answer to $ 2x + 14 > 8 + 2x $ is? a. many solutions b. no solution c. $ -6 $ 7. indicate the incorrect step. $ 2x + 4 - x = 19x - 11 $ step 1: $ x + 4 = 19x - 11 $ step 2: $ \div 19x $ $ \div 19x $ a. step 1 b. step 2 c. stepson

Accepted Answer

### Question 1
# Explanation:
## Step1: Set equations equal
Since both equal $ y $, set $ -4x + 13=\frac{1}{2}x + 4 $.
## Step2: Solve for $ x $
Add $ 4x $ to both sides: $ 13=\frac{9}{2}x + 4 $. Subtract 4: $ 9=\frac{9}{2}x $. Multiply by $ \frac{2}{9} $: $ x = 2 $.
## Step3: Find $ y $
Substitute $ x = 2 $ into $ y=-4x + 13 $: $ y=-8 + 13 = 5 $. So solution is $ (2,5) $.
# Answer: c. (2,5)

### Question 2
# Explanation:
The system is $ 2x + 3y = 9 $ and $ 2x - 5y = 3 $. The $ x $-coefficients are both 2. Subtracting the equations (or subtracting the second from the first) will eliminate $ x $, which is a common first step for elimination. Adding would not eliminate $ x $, and multiplying by 5 is not needed here.
# Answer: b. Subtract them

### Question 3
# Explanation:
## Step1: Solve the second equation for $ x $
From $ x - 5y=-13 $, we get $ x = 5y - 13 $.
## Step2: Substitute into first equation
Substitute $ x = 5y - 13 $ into $ -4x + 3y=-16 $: $ -4(5y - 13)+3y=-16 $.
## Step3: Simplify and solve for $ y $
$ -20y + 52 + 3y=-16 $ → $ -17y=-68 $ → $ y = 4 $.
## Step4: Find $ x $
Substitute $ y = 4 $ into $ x = 5y - 13 $: $ x = 20 - 13 = 7 $. So solution is $ (7,4) $.
# Answer: c. (7,4)

### Question 4
# Brief Explanations:
SpongeBob SquarePants is a sponge, so the correct answer is the option labeled "SPONGE".
# Answer: a. SPONGE

### Question 5
# Explanation:
Using substitution, since both equations are solved for $ y $, we substitute $ y = 4x - 5 $ into $ y = 2x + 3 $. This gives $ 4x - 5 = 2x + 3 $, which is the result of the first step of substitution.
# Answer: b. $ 4x - 5 = 2x + 3 $

### Question 6
# Explanation:
Simplify $ 2x + 14>8 + 2x $. Subtract $ 2x $ from both sides: $ 14>8 $. This is always true, but wait—wait, no: wait, $ 2x - 2x + 14>8 $ → $ 14>8 $, which is true, but the inequality is $ 2x + 14>2x + 8 $. Subtract $ 2x $: $ 14>8 $, which is always true? Wait, no, wait, the original inequality: $ 2x + 14>8 + 2x $. Subtract $ 2x $ from both sides: $ 14>8 $, which is a true statement, but that would mean all real numbers are solutions? But the options are "Many Solutions" (which could mean all real numbers), "No Solution", or -6. Wait, but let's check again. $ 2x + 14>2x + 8 $. Subtract $ 2x $: $ 14>8 $, which is true for all $ x $, so there are many solutions (all real numbers). But wait, maybe a mistake? Wait, no—if we subtract $ 2x $, we get $ 14>8 $, which is always true, so the inequality holds for any $ x $, so "Many Solutions" (since infinitely many solutions). But wait, the options: a. Many Solutions, b. No Solution, c. -6. So the answer is a? Wait, no—wait, maybe I made a mistake. Wait, $ 2x + 14>8 + 2x $. Subtract $ 2x $: $ 14>8 $, which is true, so the solution is all real numbers, so "Many Solutions" is correct? Wait, but maybe the problem is written wrong? Or maybe I misread. Wait, the inequality is $ 2x + 14>8 + 2x $. Yes, so subtracting $ 2x $ gives $ 14>8 $, which is always true, so there are many solutions.
# Answer: a. Many Solutions

### Question 7
# Explanation:
Step 1: $ 2x + 4 - x = 19x - 11 $ simplifies to $ x + 4 = 19x - 11 $, which is correct. Step 2: Dividing both sides by $ 19x $ is incorrect because we should isolate $ x $ by subtracting $ x $ (or $ 19x $) from both sides, not dividing by $ 19x $ (which is not a valid operation here, especially if $ x = 0 $, it's undefined). "Stepson" is a joke option. So the incorrect step is Step 2.
# Answer: b. Step 2

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Question

Explanation:

Question 1

Step1: Set equations equal

Step2: Solve for \( x \)

Step3: Find \( y \)

Step1: Solve the second equation for \( x \)

Step2: Substitute into first equation

Step3: Simplify and solve for \( y \)

Step4: Find \( x \)

Answer:

Question 2