Question

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$$\begin{cases} 3x + 7y = 2 \\\\ x = 3 \\end{cases}$$

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$$\begin{cases} 8x + 5y = 24 \\\\ y = -4x \\end{cases}$$

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$$\begin{cases} 9x - 8y = 3 \\\\ x = 3 \\end{cases}$$

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$$\begin{cases} -5x + 4y = 3 \\\\ x = 2y - 15 \\end{cases}$$

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$$\begin{cases} 5x - 4y = -10 \\\\ y = 2x - 5 \\end{cases}$$

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$$\begin{cases} -4x + 3y = -2 \\\\ y = x - 1 \\end{cases}$$

Explanation:

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System 1

Step1: Substitute $x=3$

$3(3) +7y = 2$

Step2: Simplify and solve for $y$

$9 +7y =2 \implies 7y = -7 \implies y=-1$

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System 2

Step1: Substitute $y=-4x$

$8x +5(-4x) =24$

Step2: Simplify and solve for $x$

$8x-20x=24 \implies -12x=24 \implies x=-2$

Step3: Solve for $y$

$y=-4(-2)=8$

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System3

Step1: Substitute $x=3$

$9(3)-8y=3$

Step2: Simplify and solve for $y$

$27-8y=3 \implies -8y=-24 \implies y=3$

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System4

Step1: Substitute $x=2y-15$

$-5(2y-15)+4y=3$

Step2: Simplify and solve for $y$

$-10y +75 +4y=3 \implies -6y=-72 \implies y=12$

Step3: Solve for $x$

$x=2(12)-15=9$

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System5

Step1: Substitute $y=2x-5$

$5x-4(2x-5)=-10$

Step2: Simplify and solve for $x$

$5x-8x+20=-10 \implies -3x=-30 \implies x=10$

Step3: Solve for $y$

$y=2(10)-5=15$

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System6

Step1: Substitute $y=x-1$

$-4x +3(x-1)=-2$

Step2: Simplify and solve for $x$

$-4x+3x-3=-2 \implies -x=1 \implies x=-1$

Step3: Solve for $y$

$y=-1-1=-2$

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Answer:

1. $x=3, y=-1$
2. $x=-2, y=8$
3. $x=3, y=3$
4. $x=9, y=12$
5. $x=10, y=15$
6. $x=-1, y=-2$