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:

Step1: Substitute $x=3$

$3(3) +7y = 2 \implies 9 +7y=2$

Step2: Solve for $y$

$7y=2-9=-7 \implies y=\frac{-7}{7}=-1$

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Step1: Substitute $y=-4x$

$8x +5(-4x)=24 \implies 8x-20x=24$

Step2: Solve for $x$

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

Step3: Solve for $y$

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

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Step1: Substitute $x=3$

$9(3)-8y=3 \implies 27-8y=3$

Step2: Solve for $y$

$-8y=3-27=-24 \implies y=\frac{-24}{-8}=3$

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Step1: Substitute $x=2y-15$

$-5(2y-15)+4y=3 \implies -10y+75+4y=3$

Step2: Solve for $y$

$-6y=3-75=-72 \implies y=\frac{-72}{-6}=12$

Step3: Solve for $x$

$x=2(12)-15=24-15=9$

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Step1: Substitute $y=2x-5$

$5x-4(2x-5)=-10 \implies5x-8x+20=-10$

Step2: Solve for $x$

$-3x=-10-20=-30 \implies x=\frac{-30}{-3}=10$

Step3: Solve for $y$

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

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Step1: Substitute $y=x-1$

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

Step2: Solve for $x$

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

Step3: Solve for $y$

$y=-1-1=-2$

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. $x=-1, y=-2$