1. what does a represent in the standard form equation, ax + by = c?
a. the coefficient of y
b. the constant term
c. the coefficient of x
d. none of the available answers
2. rearrange x = 3y - 3 into standard form.
a. 5y - x = -3
b. 5y - x = 3
c. x - 5y = -3
d. x + 5y = 3
3. what value of y satisfies the equation 10x - 5y = 20 when x = 3?
a. 2
b. -2
c. 1
d. 0
4. convert y + 5 = 3x into standard form.
a. x - 3y = -5
b. 3x - y = 5
c. x + 3y = 5
d. 3x + y = 5
5. a rectangle has a length of 2 times its width. if the perimeter is 48 inches, which equation represents this situation?
a. 2w + 2(2w) = 48
b. 2w + 2l = 24
c. 2w + 2(2|w|) = 48
d. 2w + 2l = 48

Question

1. what does a represent in the standard form equation, ax + by = c?
   a. the coefficient of y
   b. the constant term
   c. the coefficient of x
   d. none of the available answers
2. rearrange x = 3y - 3 into standard form.
   a. 5y - x = -3
   b. 5y - x = 3
   c. x - 5y = -3
   d. x + 5y = 3
3. what value of y satisfies the equation 10x - 5y = 20 when x = 3?
   a. 2
   b. -2
   c. 1
   d. 0
4. convert y + 5 = 3x into standard form.
   a. x - 3y = -5
   b. 3x - y = 5
   c. x + 3y = 5
   d. 3x + y = 5
5. a rectangle has a length of 2 times its width. if the perimeter is 48 inches, which equation represents this situation?
   a. 2w + 2(2w) = 48
   b. 2w + 2l = 24
   c. 2w + 2(2|w|) = 48
   d. 2w + 2l = 48

Accepted Answer

### 1. What does $ A $ represent in the standard form equation $ Ax + By = C $?
#### Brief Explanations:
In the standard form of a linear equation $ Ax + By = C $, $ A $, $ B $, and $ C $ are integers (with $ A $ non - negative usually), and $ A $ is the coefficient of the $ x $ - term. Option a says it's the coefficient of $ y $ (wrong), option b says it's the constant term (wrong), option d is incorrect as option c is correct.
#### Answer:
c. The coefficient of $ x $

### 2. Rearrange $ x = 5y - 3 $ into standard form.
#### Brief Explanations:
The standard form of a linear equation is $ Ax+By = C $. Starting with $ x = 5y - 3 $, we subtract $ 5y $ from both sides to get $ x-5y=- 3 $. Let's check the options: option a: $ 5y - x = 3 $ is equivalent to $ -x + 5y=3 $ (not the same as our result), option b: $ 5y - x=-3 $ is equivalent to $ -x + 5y=-3 $ (wrong), option d: $ x + 5y = 3 $ (wrong).
#### Answer:
c. $ x - 5y=-3 $

### 3. What value of $ y $ satisfies the equation $ 10x - 5y = 20 $ when $ x = 3 $?
#### Explanation:
## Step 1: Substitute $ x = 3 $ into the equation
Substitute $ x = 3 $ into $ 10x-5y = 20 $, we get $ 10\times3-5y = 20 $.
## Step 2: Simplify the left - hand side
$ 30-5y = 20 $
## Step 3: Solve for $ y $
Subtract 30 from both sides: $ - 5y=20 - 30=-10 $. Then divide both sides by - 5: $ y=\frac{-10}{-5}=2 $.
#### Answer:
a. 2

### 4. Convert $ y + 5 = 3x $ into standard form.
#### Brief Explanations:
The standard form is $ Ax + By = C $. Starting with $ y + 5 = 3x $, we subtract $ 3x $ and 5 from both sides (or rearrange) to get $ - 3x+y=-5 $, and then multiply both sides by - 1 to get $ 3x - y = 5 $ (we can also move terms directly: subtract $ y $ and 5 from both sides: $ 3x-y=5 $). Let's check the options: option a: $ x - 3y=-5 $ (wrong), option c: $ x + 3y = 5 $ (wrong), option d: $ 3x + y = 5 $ (wrong).
#### Answer:
b. $ 3x - y = 5 $

### 5. Convert $ y + 5 = 3x $ into standard form (re - check, same as above)
#### Brief Explanations:
As above, standard form $ Ax + By = C $. From $ y + 5 = 3x $, subtract $ 3x $ and add 5? No, better to rearrange to $ 3x-y = 5 $. Wait, no, let's do it step by step. $ y+5 = 3x\Rightarrow3x - y=5 $. Wait, the option b is $ 3x - y = 5 $, option a: $ x - 3y=-5 $ (wrong), option c: $ x + 3y = 5 $ (wrong), option d: $ 3x + y = 5 $ (wrong).
#### Answer:
b. $ 3x - y = 5 $ (Wait, no, earlier for the second question we had a different equation. Wait, the fourth question is $ y + 5 = 3x $. Let's re - arrange: $ 3x-y=5 $, which is option b.

### 6. A rectangle has a length of 2 times its width. If the perimeter is 48 inches, which equation represents this situation?
#### Explanation:
## Step 1: Define variables
Let the width of the rectangle be $ w $. Then the length $ l = 2w $.
## Step 2: Recall the perimeter formula for a rectangle
The perimeter $ P $ of a rectangle is given by $ P = 2(l + w) $.
## Step 3: Substitute $ l = 2w $ and $ P = 48 $ into the formula
Substituting, we get $ 2(2w+w)=48 $? No, wait, $ l = 2w $, so $ P = 2(l + w)=2(2w + w)=48 $? Wait, no, the options: option a: $ 2w+2(2w)=48 $ (since $ l = 2w $, perimeter $ P = 2(l + w)=2(2w+w)=2w + 2(2w)=48 $? Wait, $ 2(l + w)=2l+2w $, and $ l = 2w $, so $ 2(2w)+2w=4w + 2w = 6w $, but the formula is $ 2(l + w)=2(2w+w)=6w $. Wait, the options: option a: $ 2w+2(2w)=48 $ (which is $ 2w + 4w=6w = 48 $, correct), option b: $ 2w+2l = 24 $ (perimeter is 48, not 24, wrong), option c: $ 2w+2(2w)=48 $ is the same as option a? Wait, no, the original options: option a: $ 2w+2(2w)=48 $, option c: $ 2w + 2(2w)=48 $ (maybe a typo, but let's check the logic. Let width be $ w $, length $ l = 2w $, perimeter $ P = 2(l + w)=2(2w+w)=2w+2(2w)=48 $. So the correct equation is $ 2w + 2(2w)=48 $, which is option a (or option c, but looking at the options, option a: $ 2w+2(2w)=48 $, option c: $ 2w + 2(2w)=48 $ (maybe a typo in the original, but the correct form is $ 2w+2(2w)=48 $).
#### Answer:
a. $ 2w + 2(2w)=48 $ (assuming option a is $ 2w+2(2w)=48 $)

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QUESTION IMAGE

Question

Explanation:

1. What does \( A \) represent in the standard form equation \( Ax + By = C \)?

Step 1: Substitute \( x = 3 \) into the equation

Step 2: Simplify the left - hand side

Step 3: Solve for \( y \)

Answer:

2. Rearrange \( x = 5y - 3 \) into standard form.