Question

question 2 of 10, step 1 of 1
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.
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$$\begin{cases} 6x - 4y = 0 \\\\ -2x + 7y = -17 \\end{cases}$$

answer
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\bigcirc only one solution
\bigcirc inconsistent system
\bigcirc dependent system

Explanation:

Step1: Eliminate $x$ variable

Multiply the second equation by 3:
$$3(-2x + 7y) = 3(-17)$$
$$-6x + 21y = -51$$
Add this to the first equation $6x - 4y = 0$:
$$(6x - 4y) + (-6x + 21y) = 0 + (-51)$$
$$17y = -51$$

Step2: Solve for $y$

Divide both sides by 17:
$$y = \frac{-51}{17} = -3$$

Step3: Substitute $y=-3$ to find $x$

Use the first equation $6x - 4y = 0$:
$$6x - 4(-3) = 0$$
$$6x + 12 = 0$$
$$6x = -12$$
$$x = \frac{-12}{6} = -2$$

Answer:

Only One Solution
$x=-2$, $y=-3$