Question

variables are aligned. eliminate and make sure your solution is in the correct order.
system
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$$\begin{cases}3y - x = 2\\\\3y + x = 16\\end{cases}$$

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$$\begin{cases}2x - 3y = 4\\\\x + 3y = 29\\end{cases}$$

solution
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( , )

Explanation:

Step1: Solve first system: add equations

$$\begin{cases} 3y - x = 2 \\ 3y + x = 16 \end{cases}$$

Add the two equations:
$$(3y - x) + (3y + x) = 2 + 16$$
$$6y = 18$$

Step2: Solve for y

$$y = \frac{18}{6} = 3$$

Step3: Substitute y=3 to find x

Substitute $y=3$ into $3y - x = 2$:
$$3(3) - x = 2$$
$$9 - x = 2$$
$$x = 9 - 2 = 7$$

Step4: Solve second system: add equations

$$\begin{cases} 2x - 3y = 4 \\ x + 3y = 29 \end{cases}$$

Add the two equations:
$$(2x - 3y) + (x + 3y) = 4 + 29$$
$$3x = 33$$

Step5: Solve for x

$$x = \frac{33}{3} = 11$$

Step6: Substitute x=11 to find y

Substitute $x=11$ into $x + 3y = 29$:
$$11 + 3y = 29$$
$$3y = 29 - 11 = 18$$
$$y = \frac{18}{3} = 6$$

Answer:

First system solution: $(7, 3)$
Second system solution: $(11, 6)$