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qaws [65]
3 years ago
11

How are slopes and y-intercepts related to the number of solutions of a system of linear equations

Mathematics
1 answer:
Nina [5.8K]3 years ago
7 0
<h3>Explanation:</h3>

For a system of 2 equations in 2 unknowns, there are 3 cases:

  1. slopes are different — one solution
  2. slopes are the same and y-intercepts are different — no solutions
  3. slopes and y-intercepts are the same — infinitely many solutions

When slopes are different, the two lines intersect at <em>one</em> point, the <em>solution</em>.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence <em>no solutions</em>. If the lines are the same line, they intersect at all points, so there are <em>infinitely many solutions</em>.

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Step-by-step explanation:

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Answer:

See explanation

Step-by-step explanation:

1. Factor the function f(x)=-2x^2+16x-30:

f(x)=-2x^2+16x-30=-2x^2+6x+10x-30=-2x(x-3)+10(x-3)=-2(x-3)(x-5).

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3 0
3 years ago
Simplify (3x+2)(x-7)
vovangra [49]
The answer is
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first you must multiply or use the FOIL method (First, Outer, Inner, Last)
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this gives you -21x, then you multiply the inner terms
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To make sure this is correct simply add 20 to 60.

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