Question

related questions: lesson 4: systems of equations

select the answers for \\(x\\) and \\(y\\) after solving the system of equations using elimination method.

q. \\(\

$$\begin{cases} 7x + 22y = -28 \\\\ 3x - 11y = -12 \\end{cases}$$

\\)

a. \\((-4, 0)\\)
b. \\((-4, 1)\\)
c. \\((4, 0)\\)
d. \\((4, -1)\\)

Explanation:

Set up the system of equations

Using the Systems of Equations knowledge point

$$
LATEXBLOCK0
$$

Multiply Equation 2 to align coefficients

Using the Elimination Method knowledge point

$$ 2 \cdot (3x - 11y) = 2 \cdot (-12) \implies 6x - 22y = -24 \quad \text{(Equation 3)} $$

Add Equation 1 and Equation 3 to eliminate y

Using the Elimination Method knowledge point

$$ (7x + 22y) + (6x - 22y) = -28 + (-24) \implies 13x = -52 $$

Solve for x

Using the Elimination Method knowledge point

$$ x = \frac{-52}{13} = -4 $$

Substitute x back to solve for y

Using the Elimination Method knowledge point

$$ 3(-4) - 11y = -12 \implies -12 - 11y = -12 \implies -11y = 0 \implies y = 0 $$

Answer:

• (A) \((-4, 0)\) (Correct answer)
• (B) \((-4, 1)\)
• (C) \((4, 0)\)
• (D) \((4, -1)\)