Question

solve the system with elimination. \

$$\begin{cases} 3x + y = 9 \\\\ x + 2y = 3 \\end{cases}$$

(?, )

Explanation:

Step1: Eliminate \( y \) by multiplying the first equation

Multiply the first equation \( 3x + y = 9 \) by 2 to get \( 6x + 2y = 18 \).

Step2: Subtract the second equation from the new first equation

Subtract \( x + 2y = 3 \) from \( 6x + 2y = 18 \):
\( (6x + 2y) - (x + 2y) = 18 - 3 \)
Simplify: \( 5x = 15 \).

Step3: Solve for \( x \)

Divide both sides by 5: \( x = \frac{15}{5} = 3 \).

Step4: Substitute \( x = 3 \) into the second equation

Substitute into \( x + 2y = 3 \): \( 3 + 2y = 3 \).

Step5: Solve for \( y \)

Subtract 3 from both sides: \( 2y = 0 \), so \( y = 0 \).

Answer:

\((3, 0)\)