To solve the system of equations given by:
- \( y = -3x + 1 \) (Equation 1)
- \( -x + 2y = 9 \) (Equation 2)
we can substitute Equation 1 into Equation 2.
Substituting \( y \) from Equation 1 into Equation 2:
\[ -x + 2(-3x + 1) = 9 \]
Now simplify:
\[ -x - 6x + 2 = 9 \]
Combine like terms:
\[ -7x + 2 = 9 \]
Now, isolate \( x \) by subtracting 2 from both sides:
\[ -7x = 7 \]
Divide by -7:
\[ x = -1 \]
Now that we have \( x \), substitute it back into Equation 1 to find \( y \):
\[ y = -3(-1) + 1 \] \[ y = 3 + 1 = 4 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-1, 4) \]
To summarize:
- Solution: \( x = -1, y = 4 \)
- Point: \((-1, 4)\)