Question

y=-3x+1
-x+2y=9

Answer 1

To solve the system of equations given by:

1. \( y = -3x + 1 \) (Equation 1)
2. \( -x + 2y = 9 \) (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**: \((-1, 4)\)