Question

\\x + y = 3\\
\\x - 3y = -9\\

what is the solution \\((x, y)\\) to the given system of equations?

choose 1 answer:

a \\((-3, 0)\\)

b \\((0, 3)\\)

c \\((1, 2)\\)

d \\((9, -6)\\)

Explanation:

Express x in terms of y

$$ x + y = 3 \implies x = 3 - y $$

Substitute into the second equation

$$ (3 - y) - 3y = -9 \implies 3 - 4y = -9 \implies -4y = -12 \implies y = 3 $$

Solve for x

$$ x = 3 - 3 \implies x = 0 $$

Answer:

• (A) \((-3,0)\)
• (B) \((0,3)\) (Correct answer)
• (C) \((1,2)\)
• (D) \((9,-6)\)