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

Question

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:

• \( x = -5 \)