Question

8.
Solve the system of equations using substitution.

y = 2x – 10
y = 4x – 8


(–1, –12)


(3, 4)


(–4, –17)


(3, –4)

Answer 1

To solve the system of equations using substitution, we follow these steps:

### Given:
\[ y = 2x - 10 \]
\[ y = 4x - 8 \]

### Step 1: Set the equations equal to each other
Since both expressions equal \( y \), we set them equal to each other:
\[ 2x - 10 = 4x - 8 \]

### Step 2: Solve for \( x \)
Subtract \( 2x \) from both sides:
\[ -10 = 2x - 8 \]

Add 8 to both sides:
\[ -2 = 2x \]

Divide both sides by 2:
\[ x = -1 \]

### Step 3: Substitute \( x = -1 \) back into one of the original equations to solve for \( y \)
We can use the first equation \( y = 2x - 10 \):
\[ y = 2(-1) - 10 \]
\[ y = -2 - 10 \]
\[ y = -12 \]

### Solution:
The solution to the system of equations is:
\[ (x, y) = (-1, -12) \]

So, the correct answer is:
\[ (-1, -12) \]