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notsponge [240]
3 years ago
5

A system of linear equations has been graphed in the diagram. Determine a reasonable solution for the system of equations.

Mathematics
1 answer:
NeTakaya3 years ago
7 0

Remark

  • You have to make a couple of assumptions. The first is that the x and y axis are the same unit spacing.
  • That means that 0,1 and 1,0 are the same distance from the origin and the same would be true for 0,2 and 2,0. The minus points would have to have the same things said about them.
  • The next assumption is that the solution point is in the third quadrant. It would look something like (-   , -    )
  • The last assumption is that x is a larger number than y. x in this case means that x is less negative than y.
  • Eye balling it tells me that the x value is about 1/4 the y value.

Solution

A reasonable solution would be (-1 , - 4)

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Put the following equation in standard form and determine the quadratic, linear, and constant coefficients. -3x2 - 8 = 5x - 7
marusya05 [52]

Answer:

  • -3x² -5x -1 = 0
  • -3 (quadratic)
  • -5 (linear)
  • -1 (constant)

Step-by-step explanation:

The equation will be in standard form when terms are listed in order of decreasing degree, and the right side of the equation is 0.

<h3>Standard form</h3>

We can subtract the right-side expression from both sides to get standard form.

  -3x² -8 -(5x -7) = 5x -7 -(5x -7)

  -3x² -8 -5x +7 = 0 . . . . . . . simplify a bit

  -3x² -5x -1 = 0 . . . . . . . . . collect terms

The standard form equation can be written ...

  -3x² -5x -1 = 0

<h3>Coefficients</h3>

The quadratic coefficient is the coefficient of the term with degree 2. The quadratic coefficient is -3.

The linear coefficient is the coefficient of the term with degree 1. The linear coefficient is -5.

The constant coefficient is the coefficient of the term with no variables. The constant is -1.

__

<em>Additional comment</em>

We can make the leading coefficient positive by multiplying the equation by -1. This gives ...

  3x² +5x +1 = 0

with quadratic, linear, and constant coefficients 3, 5, 1.

This is a legitimate answer to this question. In the case of linear equations, the "standard form" has the constant on the right side of the equal sign, and the leading coefficient is required to be positive. A negative leading coefficient can sometimes lead to errors (when the sign is overlooked), so having a positive leading coefficient is often preferred.

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