Question

solve the system using elimination.\

$$\begin{cases}x + 4y = 9\\\\6x + 3y = -9\\end{cases}$$

\select the correct choice below and fill in any answer boxes in your choice.\bigcirc a. the solution is \square. (type an ordered pair.)\bigcirc b. there are infinitely many solutions.\bigcirc c. there is no solution.

Explanation:

Step1: Eliminate $x$ variable

Multiply first equation by $-6$:
$-6(x + 4y) = -6 \times 9$
$\implies -6x -24y = -54$

Step2: Add to second equation

Add new equation to $6x + 3y = -9$:
$(-6x -24y) + (6x + 3y) = -54 + (-9)$
$\implies -21y = -63$

Step3: Solve for $y$

Divide both sides by $-21$:
$y = \frac{-63}{-21} = 3$

Step4: Substitute $y=3$ to find $x$

Use first equation $x + 4y = 9$:
$x + 4(3) = 9$
$\implies x + 12 = 9$
$\implies x = 9 - 12 = -3$

Answer:

A. The solution is $(-3, 3)$. (Type an ordered pair.)