Answered

Solve for [tex]$x$[/tex] and [tex][tex]$y$[/tex][/tex]:

[tex]\[
\begin{array}{l}
y = 2 + 7x \\
-2x + 6y = 172 \\
\end{array}
\][/tex]

A. [tex]x = -74, y = 4[/tex]
B. [tex]x = 4, y = 30[/tex]
C. [tex]x = 32, y = 226[/tex]
D. [tex]x = 30, y = 4[/tex]



Answer :

GinnyAnswer
To solve the system of equations:

[tex]\[ \begin{array}{l} y = 2 + 7x \quad \quad \quad \quad (1) \\ -2x + 6y = 172 \quad \quad (2) \end{array} \][/tex]

we will follow these steps:

### Step 1: Express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] from Equation (1):

Equation (1) is already solved for [tex]\( y \)[/tex]:

[tex]\[ y = 2 + 7x \][/tex]

### Step 2: Substitute [tex]\( y \)[/tex] into Equation (2):

Now substitute [tex]\( y = 2 + 7x \)[/tex] into Equation (2):

[tex]\[ -2x + 6(2 + 7x) = 172 \][/tex]

### Step 3: Simplify the substituted equation:

[tex]\[ -2x + 6 \cdot 2 + 6 \cdot 7x = 172 \][/tex]

[tex]\[ -2x + 12 + 42x = 172 \][/tex]

Combine like terms:

[tex]\[ 40x + 12 = 172 \][/tex]

### Step 4: Solve for [tex]\( x \)[/tex]:

Subtract 12 from both sides:

[tex]\[ 40x = 160 \][/tex]

Divide both sides by 40:

[tex]\[ x = 4 \][/tex]

### Step 5: Substitute [tex]\( x \)[/tex] back into Equation (1) to solve for [tex]\( y \)[/tex]:

Plugging [tex]\( x = 4 \)[/tex] back into [tex]\( y = 2 + 7x \)[/tex]:

[tex]\[ y = 2 + 7 \cdot 4 \][/tex]

[tex]\[ y = 2 + 28 \][/tex]

[tex]\[ y = 30 \][/tex]

### Conclusion:

The solution to the system of equations is:

[tex]\[ x = 4 \quad \text{and} \quad y = 30 \][/tex]

So the correct answer is:

[tex]\[ \begin{array}{l} x=4, y=30 \end{array} \][/tex]