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Arte-miy333 [17]
2 years ago
7

Find the solution of y=x+3 and y=2x+6

Mathematics
2 answers:
lisabon 2012 [21]2 years ago
3 0

Answer:

x = 3 and y = 0

Step-by-step explanation:

To find the solution where you have two equations is called a System of Equations.

What you do is you notice there are two equations and the let both equations equal each other. We can do this because both equations start with a y. These "y" work like puzzles and you can connect the "x+3" and "2x + 6" together. Then solve for it. Here's what i mean,

y = x+3

y = 2x+6

Now connecting them,

x+3 = 2x+6

Subtract x from both sides

3 = x + 6

Subtract 6 from both sides,

x = -3

Now solve for y,

y = -3 + 3 = 0

So our solution is x = 3 and y = 0.

olasank [31]2 years ago
3 0

Answer:

  (x, y) = (-3, 0)

Step-by-step explanation:

Substitution or elimination work well for solving this system of equations.

__

<h3>Elimination</h3>

Subtract the first equation from the second.

  (y) -(y) = (2x +6) -(x +3)

  0 = x +3

  -3 = x . . . . . . . subtract 3

  y = (-3) +3 = 0 . . . . use the first equation to find y

  (x, y) = (-3, 0)

__

<h3>Substitution</h3>

Use the second equation to substitute for y in the first.

  2x +6 = x +3

  x = -3 . . . . . . . . . subtract x+6 from both sides

  y = (-3) +3 = 0 . . . . find y using the first equation

  (x, y) = (-3, 0)

__

A graphing calculator answers these quickly.

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cupoosta [38]

Answer:

z = -12

Step-by-step explanation:

The given system of equations is:

xy/(x + y) = 1 ...........................(1)

xz/(x + z) = 2...........................(2)

yz/(y + z) = 3...........................(3)

From (1): x + y = xy

=> y = xy - x

y = x(y - 1)

x = y/(y - 1).......................................(4)

From (2): 2(x + z) = xz

=> 2x + 2z = xz

2x = xz - 2z

2x = z(x - 2)

z = 2x/(x - 2) ....................................(5)

From (3): 3(y + z) = yz

=> 3y + 3z = yz

3y = yz - 3z

3y = z(y - 3)

z = 3y/(y - 3)....................................(6)

Comparing (5) and (6)

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

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

2xy - 6x = 3xy - 6y

6(y - x) = xy .................................(7)

But from (1): xy = x + y

Using this in (7), we have

6(y - x) = x + y

6y - y - 6x - x = 0

5y - 7x = 0

5y = 7x

x = 5y/7................................................(8)

Using this in (4)

5y/7 = y/(y - 1)

1/(y - 1) = 5/7

(y - 1) = 7/5

y = 1 + 7/5

y = 12/5..........................................(9)

Using this in (8)

x = 5(12/5)/7 = 12/7 .......................(10)

Using (10) in (5)

z = 2x/(x - 2)

z = 2(12/7) ÷ (12/7 - 2)

= 24/7 ÷ -2/7

= 24/7 × (-7/2)

= -24/2 = -12

z = -12.

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