3x-y=7 x+3y=9

To solve the system of equations

1. \( 3x - y = 7 \) (Equation 1)
2. \( x + 3y = 9 \) (Equation 2)

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

First, let's manipulate the equations to eliminate one variable. We can start by expressing both equations in standard form.

Step 1: Rearranging the equations.

From Equation 1:
\[ y = 3x - 7 \]

From Equation 2:
\[ 3y = 9 - x \]
\[ y = \frac{9 - x}{3} \]

Step 2: Substitute.

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

\[ 3(3x - 7) = 9 - x \]

Step 3: Simplifying the equation.

Expanding gives:

\[ 9x - 21 = 9 - x \]

Now, add \( x \) to both sides:

\[ 9x + x - 21 = 9 \]

Combine like terms:

\[ 10x - 21 = 9 \]

Now add 21 to both sides:

\[ 10x = 30 \]

Step 4: Solve for \( x \).

Dividing both sides by 10:

\[ x = 3 \]

Step 5: Substitute \( x \) back into one of the original equations to find \( y \).

Let's use Equation 1:

\[ 3(3) - y = 7 \]

This simplifies to:

\[ 9 - y = 7 \]

Now, isolate \( y \):

\[ -y = 7 - 9 \]
\[ -y = -2 \]
\[ y = 2 \]

Solution:

So, the solution to the system of equations is:

\[ x = 3 \]
\[ y = 2 \]

Therefore, the solution is \( (3, 2) \).