Question

x = 3y - 7
y = x + 1

Answer 1

To solve the system of equations given by:

1. \( x = 3y - 7 \)
2. \( y = x + 1 \)

We can substitute the expression for \( y \) from the second equation into the first equation.

1. Substitute \( y \) in the first equation:
\[
x = 3(x + 1) - 7
\]

2. Distribute on the right side:
\[
x = 3x + 3 - 7
\]

3. Simplify the right side:
\[
x = 3x - 4
\]

4. Move \( 3x \) to the left side:
\[
x - 3x = -4
\]
\[
-2x = -4
\]

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

Now that we have \( x \), we can substitute it back into the second equation to find \( y \):
\[
y = x + 1 = 2 + 1 = 3
\]

So the solution to the system of equations is:
\[
x = 2, \quad y = 3
\]