write the equation in the standard linear equation form ($ax + by = $ blank, write yes if it is linear. if the answer is no, explain why.
7) $\frac{y}{3}+x = 5$ explain if no.
8) $3x + 5^{y}=8$ explain if no.
9) $x + 9y^{2}=1$ explain if no.
10) $1+\frac{7}{x}=y$ explain if no.
11) $7 + x = 2y$ explain if no.

Question

Accepted Answer

### Problem 7
# Explanation:
## Step1: Recall standard linear form
The standard linear equation form is $Ax + By = C$, where $A$, $B$, and $C$ are constants, and the exponents of $x$ and $y$ are 1.
## Step2: Transform the given equation
Given $\frac{y}{3}+x = 5$, multiply both sides by 3 to eliminate the fraction: $y + 3x = 15$, which can be rewritten as $3x + y = 15$. This is in the form $Ax + By = C$ with $A = 3$, $B = 1$, $C = 15$, and the exponents of $x$ and $y$ are 1.
# Answer:
Yes, and the standard form is $3x + y = 15$

### Problem 8
# Explanation:
## Step1: Recall linear equation definition
A linear equation in two variables $x$ and $y$ has the form $Ax + By = C$ where $A$, $B$, $C$ are constants, and the exponents of $x$ and $y$ are 1.
## Step2: Analyze the given equation
The equation is $3x + 5^{y}=8$. Here, the term $5^{y}$ has $y$ in the exponent, not as a linear term (exponent of $y$ is not 1). So it does not fit the linear equation form.
# Answer:
No. Explanation: The term $5^{y}$ has $y$ in the exponent, so the equation is not linear (linear equations have $x$ and $y$ with exponent 1).

### Problem 9
# Explanation:
## Step1: Recall linear equation form
Linear equations in two variables have the form $Ax + By = C$ with exponents of $x$ and $y$ equal to 1.
## Step2: Analyze the given equation
The equation is $x + 9y^{2}=1$. The term $9y^{2}$ has $y$ with an exponent of 2, not 1. So it does not satisfy the linear equation form.
# Answer:
No. Explanation: The term $9y^{2}$ has $y$ with exponent 2, so the equation is not linear.

### Problem 10
# Explanation:
## Step1: Recall linear equation definition
A linear equation in two variables $x$ and $y$ has the form $Ax + By = C$ where $A$, $B$, $C$ are constants, and $x$ and $y$ are to the first power and not in the denominator.
## Step2: Analyze the given equation
The equation is $1+\frac{7}{x}=y$, which can be rewritten as $y = 1+\frac{7}{x}$ or $xy=x + 7$ (after multiplying both sides by $x$, $x
eq0$). Here, $x$ is in the denominator (or when rewritten, the term $xy$ has a product of $x$ and $y$, and $x$ was in the denominator initially), so it does not fit the linear equation form.
# Answer:
No. Explanation: $x$ is in the denominator ($\frac{7}{x}$), so the equation is not linear (linear equations have $x$ and $y$ as linear terms, not in denominators).

### Problem 11
# Explanation:
## Step1: Recall standard linear form
The standard linear equation form is $Ax + By = C$, with $A$, $B$, $C$ as constants and exponents of $x$ and $y$ equal to 1.
## Step2: Transform the given equation
Given $7 + x = 2y$, rearrange it to $x - 2y=- 7$, which is in the form $Ax + By = C$ with $A = 1$, $B=-2$, $C = - 7$, and the exponents of $x$ and $y$ are 1.
# Answer:
Yes, and the standard form is $x - 2y=-7$ (or $x - 2y + 7 = 0$, or other equivalent rearrangements)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 7

Step1: Recall standard linear form

Step2: Transform the given equation

Step1: Recall linear equation definition

Step2: Analyze the given equation

Step1: Recall linear equation form

Step2: Analyze the given equation

Answer:

Problem 8