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Thepotemich [5.8K]
3 years ago
8

I need a little help! Can someone check my work? It's a written response with linear systems.

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
5 0

Answer:

I'd say you need to be more specific.

Step-by-step explanation:

"Different" doesn't tell you much.

Consider the equations ...

  • y = 2x + 1
  • 4x - 2y = -2

These equations are "different", but they are <em>dependent</em>.

_____

I'd mentally (or actually) put the equations in the same form and compare the coefficients of x and y. If they have different ratios, the system is independent and consistent.

If they have the same ratio, the system will not have a single solution. Whether there is no solution or an infinite number of solutions depends on the constant, which I would examine next.

The system above can be put in the form

  • 2x -y = -1
  • 4x -2y = -2

In both cases, the ratio of the x coefficient to the y coefficient is 2/-1 = 4/-2 = -2. This means the lines are at least parallel, if not identical. The numbers in the second equation are all 2 times the numbers in the first equation, so the equations are <em>dependent</em>, and there are an infinite number of solutions. (Both describe the same line.)

If the second equation were 4x -2y = 1, then the two equations would be describing parallel lines, so they would be called <em>inconsistent</em>.

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