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denis23 [38]
2 years ago
7

Y=-x+5 x-y=-9 Solve the system?

Mathematics
2 answers:
hram777 [196]2 years ago
4 0

Answer:

x=-2 y=7

Step-by-step explanation:

Oksanka [162]2 years ago
4 0

Answer:

x=-2 \quad and \quad y=7.

Step-by-step explanation:

\left\{\begin{matrix} y=-x+5 \\  x-y=-9\end{matrix}\right.\\\\\Rightarrow \left\{\begin{matrix} x+y=5 & (1)\\  x-y=-9 & (2)\end{matrix}\right.\\(1) + (2) \Rightarrow 2x=-4 \Rightarrow x=-4:2=-2\\Replace \quad x=-2\quad in \quad(1) \Rightarrow y=5-(-2)=7\\Therefore, \\x=-2 \quad and \quad y=7.

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Find an equation of the line containing the centers of the two circles whose equations are given below.
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Answer:

<h2><em>3y+x = -5</em></h2>

Step-by-step explanation:

The general equation of a circle is expressed as x²+y²+2gx+2fy+c = 0 with centre at C (-g, -f).

Given the equation of the circles x²+y²−2x+4y+1  =0  and x²+y²+4x+2y+4  =0, to  get the centre of both circles,<em> we will compare both equations with the general form of the equation above as shown;</em>

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2gx = -2x

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Divide both sides by 2:

2g/2 = -2/2

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The centre of the circle is (-(-1), -2) = (1, -2)

For the circle with equation x²+y²+4x+2y+4  =0:

2gx = 4x

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Divide both sides by 2:

2g/2 = 4/2

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Next is to find the equation of a line containing the two centres (1, -2) and (-2.-1).

The standard equation of a line is expressed as y = mx+c where;

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c is the intercept

Slope m = Δy/Δx = y₂-y₁/x₂-x₁

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The slope of the line is -1/3

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y = -1/3 x + (-5/3)

y = -x/3-5/3

Multiply through by 3

3y = -x-5

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<em>Hence the equation of the line containing the centers of the two circles is 3y+x = -5</em>

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