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3 years ago

What is the solution to the system of equations? y = x +2 y = 3x -2

Mathematics

1 answer:

Mrrafil [7]3 years ago

7 0

Answer:

x=2 and y= 4

Step-by-step explanation:

y = x +2 ----------(i)

y = 3x -2--------(ii)

Now, comparing (i) and (ii)

x+2= 3x-2

=>x-3x = -2-2

=>-2x= -4

=>2x= 4

=>x= 2

From eq (i)

y= x+2 = 2+2= 4

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Carter draws one side of equilateral △PQR on the coordinate plane at points P(-3,2) and Q(5,2). Which ordered pair is a possible

Law Incorporation [45]

Step-by-step explanation:

Hey, there!!!

Let me simply explain you about it.

We generally use the distance formula to get the points.

let the point R be (x,y)

As it an equilateral triangle it must have equal distance.

now,

let's find the distance of PQ,

we have, distance formulae is;

$pq = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} }$

$or \: \sqrt{( {5 + 3)}^{2} + ( {2 - 2)}^{2} }$

By simplifying it we get,

$8$

Now,

again finding the distance between PR,

$pr = \sqrt{( {x2 - x1}^{2} + ( {y2 - y1)}^{2} }$

or,

$\sqrt{( {x + 3)}^{2} + ( {y - 2)}^{2} }$

By simplifying it we get,

$= \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 }$

now, finding the distance of QR,

$qr = \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2} }$

or, by simplification we get,

$\sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 }$

now, equating PR and QR,

$\sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13} = \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 }$

we cancelled the root ,

${x}^{2} + {y}^{2} + 6x - 4y + 13 = {x}^{2} + {y}^{2} -10x - 4y + 29$

or, cancelling all like terms, we get,

6x+13= -10x+29

16x=16

x=16/16

Therefore, x= 1.

now,

equating, PR and PQ,

$\sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } = 8}$

cancel the roots,

${x}^{2} + {y}^{2} + 6x - 4y + 13 = 8$

now,

(1)^2+ y^2+6×1-4y+13=8

or, 1+y^2+6-4y+13=8

y^2-4y+13+6+1=8

or, y(y-4)+20=8

or, y(y-4)= -12

either, or,

y= -12 y=8

Therefore, y= (8,-12)

by rounding off both values, we get,

x= 1

y=(8,-12)

So, i think it's (1,8) is your answer..

Hope it helps...

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Step-by-step explanation:

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3 years ago

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mars1129 [50]

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Step-by-step explanation:

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5 0

3 years ago

Read 2 more answers

A one-way train ticket from New York to Los Angeles costs $197 for a reclining seat, and $490 for a twin-sharing room. How much

Alex777 [14]

The total cost if x passengers booked reclining seats and one fifths y passengers booked twin-sharing rooms is (197x + 98y) dollars

Solution:

Given that,

Cost for reclining seat = $ 197

Cost for twin sharing room = $ 490

We have to find the cost if x passengers booked reclining seats and one fifths y passengers booked twin-sharing rooms

Cost for reclining room when "x" passengers booked is:

Cost for reclining room = $ 197x

Cost when One fifths y passengers booked twin-sharing rooms

Cost for twin sharing room = $\frac{1}{5} \times y \times 490$

Cost for twin sharing room = 98y

Total cost is given as:

Total cost = Cost for reclining room "x" passengers + Cost for twin sharing room for one fifths y passengers

$Total\ cost = 197x + 98y$

Thus total cost is (197x + 98y) dollars

4 0

3 years ago