Question

solve the system of equations $2x + 3y = 6$ and $-3x - 5y = -12$ by combining the equations.
\boxed{} $(2x + 3y = 6)$
\boxed{} $(-3x - 5y = -12)$
$\

$$\begin{align*} 2x + 3y &= 6\\\\ -3x - 5y &= -12\\\\ \\hline \\boxed{}x + \\boxed{}y &= \\boxed{} \\end{align*}$$

$ try
answer attempt 1 out of 2
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Explanation:

Step1: Eliminate x, scale equations

Multiply first equation by 3: $3(2x + 3y = 6) \implies 6x + 9y = 18$
Multiply second equation by 2: $2(-3x - 5y = -12) \implies -6x - 10y = -24$

Step2: Add scaled equations

Add the two new equations:
$$(6x + 9y) + (-6x - 10y) = 18 + (-24)$$
Simplify: $-y = -6$

Step3: Solve for y

Multiply both sides by -1: $y = 6$

Step4: Substitute y into first equation

Substitute $y=6$ into $2x + 3y = 6$:
$2x + 3(6) = 6 \implies 2x + 18 = 6$

Step5: Solve for x

Subtract 18, then divide by 2:
$2x = 6 - 18 = -12 \implies x = \frac{-12}{2} = -6$

Filled coefficients for combination:

Top blank: $3$, Bottom blank: $2$
Combined equation: $0x + (-1)y = -6$

Final solution:

$x = -6$, $y = 6$

Answer:

Step1: Eliminate x, scale equations

Multiply first equation by 3: $3(2x + 3y = 6) \implies 6x + 9y = 18$
Multiply second equation by 2: $2(-3x - 5y = -12) \implies -6x - 10y = -24$

Step2: Add scaled equations

Add the two new equations:
$$(6x + 9y) + (-6x - 10y) = 18 + (-24)$$
Simplify: $-y = -6$

Step3: Solve for y

Multiply both sides by -1: $y = 6$

Step4: Substitute y into first equation

Substitute $y=6$ into $2x + 3y = 6$:
$2x + 3(6) = 6 \implies 2x + 18 = 6$

Step5: Solve for x

Subtract 18, then divide by 2:
$2x = 6 - 18 = -12 \implies x = \frac{-12}{2} = -6$

Filled coefficients for combination:

Top blank: $3$, Bottom blank: $2$
Combined equation: $0x + (-1)y = -6$

Final solution:

$x = -6$, $y = 6$