3х-y=-1 -x+2y=7

To solve the system of equations given by:

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

we can use either the substitution method or the elimination method. Here, I'll use the substitution method.

Step 1: Solve Equation 1 for \( y \)

From Equation 1, we can rearrange it to express \( y \) in terms of \( x \):

\[ y = 3x + 1 \quad (1) \]

Step 2: Substitute \( y \) into Equation 2

Now, substitute \( y \) from equation (1) into Equation 2:

\[ -x + 2(3x + 1) = 7 \]

Step 3: Simplify and solve for \( x \)

\[ -x + 6x + 2 = 7 \]

Combine like terms:

\[ 5x + 2 = 7 \]

Subtract 2 from both sides:

\[ 5x = 5 \]

Now, divide by 5:

\[ x = 1 \]

Step 4: Substitute \( x \) back to find \( y \)

Now substitute \( x = 1 \) back into Equation (1) to find \( y \):

\[ y = 3(1) + 1 \] \[ y = 3 + 1 = 4 \]

Step 5: Write the solution

The solution to the system of equations is:

\[ x = 1, \quad y = 4 \]

Final answer: \((x, y) = (1, 4)\)