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PilotLPTM [1.2K]
3 years ago
6

1) Graph both equation and identify the point of intersection. y=2x+3 x+2y=8

Mathematics
1 answer:
Verizon [17]3 years ago
5 0

Answer:

Intersection Point: (0.4, 3.8)

General Formulas and Concepts:

<u>Algebra I</u>

  • Solving systems of equations by graphing

Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = 2x + 3

x + 2y = 8

<u>Step 2: Graph</u>

<em>Where the 2 lines intersect is the solution set to the systems of equations.</em>

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Answer: (x + 6)² + (y + 5)² = 17

Explanation:

1)  The equation of a circle is: (x - a)² + (y - b)² = r², wnere:
a is the x-coordinate of the center of the circleb is the y-coordinate of the center of the circler is the radius of the circle
2) Since the points (-7,-1) and (-5,9) define a diameter, you can find the center of the circle as the mid point of the diameter:
x-coordinate of the mid point = (-7 - 5) / 2 = - 12 / 2 = - 6
y-coordinate of the mid point = (-9 - 1)/ 2 = - 10 / 2 = - 5

Therefore, the center of the circle is (-6,-5)

3) The radius of the center is half the diameter.
The length of the diameter is found using the formula for the distance between two points applied to the two endopoints given:
diameter² = (7 - 5)² + (- 1 + 9)² = 2² + 8² = 4 + 64 = 68

⇒diameter = √68 = 2√17

⇒ radius = diamter / 2 = 2√17 / 2 = √17

4) Now you can replace the coordinates of the center and the radius into the equation:
(x + 6)² + (y + 5)² = 17


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