2x-y=3. X+y=9

Step 1: Label the given equations.

$2x - y = 3 \quad (1)$

$x + y = 9 \quad (2)$

Step 2: Add equation (1) and equation (2) to eliminate y.

Formula: $(2x - y) + (x + y) = 3 + 9$

Substitute: $2x + x - y + y = 12$

Simplify: $3x = 12$

Step 3: Solve for x.

$x = \frac{12}{3}$

$x = 4$

Step 4: Substitute x = 4 into equation (2).

Formula: $x + y = 9$

Substitute: $4 + y = 9$

Simplify: $y = 9 - 4$

$y = 5$

Step 5: Verify the solution in equation (1).

Substitute x = 4 and y = 5: $2(4) - 5 = 8 - 5$

$8 - 5 = 3$

The solution checks out.

Final answer: $x = 4$, $y = 5$

x=4,\ y=5