solve the system: 2y=x+16 and 5x+10y=0?

Answer 1

2y = x + 16 - - - - -Equation 1
5x + 10y = 0- - - - Equation 2
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Rearrange equation 1

2y = x + 16

-x + 2y = x + 16 - x

-x + 2y = 16 - - - -equation 1 rearranged
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Multiply equation 1 rearranged by 5

5(-x) + 5(2y) = 5(16)

- 5x + 10y = 80- - - - New equation 1

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Elimination of x new equation 1 and equation 2

- 5x + 10y = 80
5x + 10y = 0
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20y = 80

20y/20 = 80/20

y = 4

The answer is y = 4

Insert the y value into equation 1

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Solving for x

2y = x + 16

2(4) = x + 16

8 = x + 16

8 - 16 = x + 16 - 16

-8 = x

The answer is x = - 8

Insert the x value into equation 1

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Check for equation 1

2y = x + 16

2(4) = -8 + 16

8 = 8

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Check for equation 2

5x + 10y = 0

5(- 8) + 10(4) = 0

-40 + 40 = 0

0 = 0

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The solution set is { -8, 4 }

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Answer 2

If 2y=x+16, then 10y=5x+80.
Substitiute this into second equation.
5x+(5x+80)=0
10x+80=0
10x= -80
x= -8

Substitute value for x into first equation.
2y=(-8)+16
2y=8
y=4

Check solutions in both equations
2(4)= (-8) + 16
8=8

5(-8)+10(4)=0
-40+40=0
0=0

I explained how to do it basically; the trick is substitution. There are other possible ways of solving it, however, such as elimination.

Answer 3

first get x and y on the same side. and lets say 16=2y-x is equation (1) and 0=5x+10y is equation (2).
Multiply (2) by -5. Then add the equations together to eliminate y.
0= 5x+10y
-80= -10y+5x

-80=10x -solve for x
x= -8.

Now put x into either equation (I choose (2)) and solve for y.

5(-8)+10y=0
-40+10y=0
10y=40
y=4

So x= -8 and y= 4.

Answer 4

2y=x+16 and 5x+10y=0
y = (x/2) + 8
plug y into the second equation
5x + 10[(x/2) + 8] = 0
5x + 5x + 80 = 0
10x = -80
x = -8
y = 4

ANSWER
x = -8
y = 4

Answer 5

x = -8
y = 4

Answer 6

y=4

x=-8