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inn [45]
3 years ago
8

Which point is the solution to the following system of equations? x2 + y2 = 13 2x - y = 4

Mathematics
2 answers:
stealth61 [152]3 years ago
8 0

Answer with Step-by-step explanation:

2x-y=4  ⇒y=2x-4

x²+y²=13

⇒ x²+(2x-4)²=13

⇒ x²+4x²+16-16x=13

⇒ 5x²-16x+3=0

⇒ 5x²-15x-x+3=0

5x(x-3)-1(x-3)=0

⇒ (5x-1)(x-3)=0

either 5x-1=0 or x-3=0

x=1/5 or x=3

when x=1/5=0.2, y=2/5-4 i.e. y=-3.6

when x=3, y=2

Hence, solution of x²+y²=13 and 2x-y=4 is:

x=0.2,y= -3.6  and x=3,y=2

         

Anit [1.1K]3 years ago
4 0
There are two solutions.
.. (3, 2)
.. (0.2, -3.6)

_____
If you're choosing possibilities from a list, trying them in the equations usually gives quick results.

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Over [174]

Remark

I think you want us to do both 3 and 4


Three

QR is 4 points going left from the y axis + 2 points going right from the y axis.

QR = 6 units long.


RT is 4 units above the x axis and 3 units below the x axis

RT = 7 units long


TS = 3 units. For this one you just go from T to S. The graph really helps you. You just need to count.


Problem 4

You need to find the area of the combined figure. You could do it as a trapezoid, which might be the easiest way. I'll do that first.


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Comment

You could break this up into a rectangle + a triangle

Find the area of QRTU and add the Area of triangle RTS


<em>Area of the rectangle </em>= L * W

L = RT = 7

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Area = 7 *6 = 42


<em>Area of the triangle</em> = 1/2 * B * H

B = TS = 3

H = RT =7

Area = 1/2 * 3 * 7

Area = 1/2 * 21

Area = 10.5


Total Area = 42 + 10.5 = 52.5 Both answers agree.

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