How do you solve the system of equations ${(y =7 - x), (x^2 + y^2 = 65):}$ ?

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How do you solve the system of equations ${(y =7 - x), (x^2 + y^2 = 65):}$ ?

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Answer 1 · 2017-03-15T22:29:22

There are two points that are solutions, $(8,-1) and (-1,8)$

Explanation:

Given:

$y^2+x^2=65 and y + x = 7$

Write the line as y as a function of x

$y^2+x^2=65 and y = 7-x$

Substitute $(7 -x)$ for y into the circle:

$(7-x)^2+x^2=65$

Square first term:

$49-14x+x^2+x^2=65$

$2x^2-14x-16=0$

$x^2-7x-8=0$

$(x-8)(x+1)=0$

$x = 8 and x = -1$

Find the corresponding y values, using the equation, $y = 7-x$

y = -1 and y = 8

Answer 2 · 2017-03-15T22:32:35

$(8, -1);(-1,8)$

Explanation:

From the second equation, we have $y = 7 - x$ . Substituting:

$(7- x)^2 + x^2 = 65$

$49 - 14x + x^2 + x^2 = 65$

$2x^2 - 14x - 16 = 0$

$2(x^2 - 7x - 8) = 0$

$x^2 - 7x - 8 = 0$

$(x - 8)(x + 1) = 0$

$x = 8 and -1$

Since this system involves the equation of a circle (e.g $x^2 + y^2 = 65$ ), the solution set will be of the form $(a, b); (b, a)$ .

The solution set therefore is $(8, -1);(-1, 8)$ .

Hopefully this helps!

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How do you solve the system of equations ${(y =7 - x), (x^2 + y^2 = 65):}$ ?

2 Answers

Explanation:

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you solve the system of equations {(y =7 - x), (x^2 + y^2 = 65):}{(y =7 - x), (x^2 + y^2 = 65):}?

2 Answers

Explanation:

Explanation:

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Impact of this question

How do you solve the system of equations ${(y =7 - x), (x^2 + y^2 = 65):}$ ?