Question

Solve the system of equations 3x + y = 3 and 7x + 2y = 1.

1. Solve for the variable y in the first equation:     y = 3 − 3x

2. Substitute the value for y into the second equation:  7x + 2(3 − 3x) = 1

3. Solve for x: x =

Answer 1

Let's go through the steps to solve the system of equations given:

We have the equations:
1. \( 3x + y = 3 \)
2. \( 7x + 2y = 1 \)

### Step 1: Solve for \( y \) in the first equation
From the first equation:
\[
y = 3 - 3x
\]

### Step 2: Substitute the value for \( y \) into the second equation
Now substitute \( y = 3 - 3x \) into the second equation:
\[
7x + 2(3 - 3x) = 1
\]

Expanding the equation:
\[
7x + 6 - 6x = 1
\]

### Step 3: Solve for \( x \)
Combine like terms:
\[
(7x - 6x) + 6 = 1
\]
\[
x + 6 = 1
\]

Now, isolate \( x \):
\[
x = 1 - 6
\]
\[
x = -5
\]

Thus, the solution for \( x \) is:
\[
x = -5
\]

### Summary of the solution:
- \( x = -5 \)