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torisob [31]
3 years ago
11

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..

<em>Hope it helps</em><em>.</em><em>.</em><em>.</em>

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350

Step-by-step explanation:

The difference is 35, she's spending 35 everyday

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Step-by-step explanation:

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5 0
2 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

<em><u>Solution:</u></em>

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

<em><u>Cost for reclining room when "x" passengers booked is:</u></em>

Cost for reclining room = $ 197x

<em><u>Cost when One fifths y passengers booked twin-sharing rooms</u></em>

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

Cost for twin sharing room = 98y

<em><u>Total cost is given as:</u></em>

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

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