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x = 3y - 7

y = x + 1

1 answer

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: \[ x = 2, \quad y = 3 \]