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ss7ja [257]
3 years ago
9

Solve the system (x-1)²+(y-2)²=2² and y=2x+2.

Mathematics
1 answer:
Likurg_2 [28]3 years ago
3 0

Answer:

  (x, y) = (-0.6, 0.8)  or  (1, 4)

Step-by-step explanation:

Use the second equation to substitute for y in the first.

 (x -1)² +((2x +2) -2)² = 4

  x -2x +1 + 4x² = 4 . . . . . . . eliminate parentheses

  5x² -2x -3 = 0 . . . . . . . . . . subtract 4, collect terms

Now we can rearrange the middle term to ease factoring by grouping.

  (5x² -5x) +(3x -3) = 0

  5x(x -1) +3(x -1) = 0

  (5x +3)(x -1) = 0

The values of x that make these factors zero are ...

  x = -3/5, x = 1

The corresponding values of y are ...

  y = 2(-3/5)+2 = 4/5 . . . . for x = -3/5

  y = 2(1) +2 = 4 . . . . . . . . for x = 1

The solutions are: (x, y) = (-3/5, 4/5) or (1, 4).

___

A graphing calculator verifies these solutions.

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The attached graph represents the graph of f(x) = (x - 1)^2 - 2

<h3>How to plot the graph?</h3>

The equation is given as:

f(x) = (x - 1)^2 - 2

Next, we set x to -2, -1, 0, 1 and 2.

So, we have:

f(-2) = (-2 - 1)^2 - 2 = 7

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This means that the table of values is

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1     -2

2    -1

Next, we plot the above points and connect them.

See attachment for the graph of f(x) = (x - 1)^2 - 2

Read more about graphs and functions at:

brainly.com/question/4025726

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