Question

select the correct answer.

what is the solution to this system of equations?
\\x = 12 - y\\
\\2x + 3y = 29\\

• \\(x = 8, y = 4\\)
• \\(x = 6, y = 6\\)
• \\(x = 7, y = 5\\)
• \\(x = 9, y = 3\\)

Explanation:

⚡ Using what you learned: solving systems by substitution

Step 1: Substitute the first equation into the second

$$ 2(12 - y) + 3y = 29 $$

Step 2: Solve for \( y \)

$$ 24 - 2y + 3y = 29 $$

$$ 24 + y = 29 $$

$$ y = 5 $$

Step 3: Solve for \( x \)

$$ x = 12 - 5 $$

$$ x = 7 $$

Answer:

\( x = 7, y = 5 \)