Question

use the method of elimination to solve the following system of equations. if the system is dependent, express the solution set in terms of one of the variables. leave all fractional answers in fraction form. \

$$\begin{cases} 3x - 6y = -12 \\\\ -5x + 8y = 22 \\end{cases}$$

selecting an option will display any text boxes needed to complete your answer. \bigcirc only one solution \bigcirc inconsistent system \bigcirc dependent system

Explanation:

Step1: Eliminate x, scale first eq.

Multiply first equation by 5:
$$15x - 30y = -60$$

Step2: Scale second eq. to match x

Multiply second equation by 3:
$$-15x + 24y = 66$$

Step3: Add equations to eliminate x

Add the two new equations:
$$(15x - 30y) + (-15x + 24y) = -60 + 66$$
$$-6y = 6$$

Step4: Solve for y

Divide both sides by -6:
$$y = \frac{6}{-6} = -1$$

Step5: Substitute y into first eq.

Substitute $y=-1$ into $3x - 6y = -12$:
$$3x - 6(-1) = -12$$
$$3x + 6 = -12$$

Step6: Solve for x

Subtract 6, then divide by 3:
$$3x = -12 - 6 = -18$$
$$x = \frac{-18}{3} = -6$$

Answer:

Only One Solution
$x=-6$, $y=-1$