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katrin2010 [14]
2 years ago
10

7x-3y=-12. Name 2 possible answers for (x,y)

Mathematics
1 answer:
anzhelika [568]2 years ago
6 0

Answer:

x = (-12/7 , 0)

y= (0,4)

Step-by-step explanation:

Plug y=0 into the equation and solve the resulting equation 7x=−12 for x

7x = -12

/7      /7

x = -12/7     and y =0

Plug x=0 into the equation and solve the resulting equation −3y=−12 for y

-3y = -12

/-3     -3

Y = 4        and X = 0

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adoni [48]

Answer:

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Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

__

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

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__

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

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The second piece can be written ...

  f(x) = -3x +14 for x > 5

__

<h3>Whole function</h3>

Putting these pieces together, we have ...

  \boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}

_____

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Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

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2 years ago
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