Solution X and Y?

Question

-4x - 5y = -21
4x + 4y = 16

-2x + y = 14
4x - 4y = -36

Thank you so much

Answer 1

1st one:

add the 2 equations
(-4x + 4x) cancels
(-5y + 4y) = -y
(-21 + 16) = -5

therefore y = 5
substitute y = 5 into one of the equation

4x + 4(5) = 16
4x + 20 = 16
4x = 16 - 20
4x = -4
x = -1

2nd one:

multiply the first equation by 2 since no addition can cancel x or y

-4x + 2y = 28
the other equation remains the same : 4x - 4y = -36

add the 2 equations cancelling x

2y - 4y = 28 - (-36)
-2y = 64
y = - 32

substitute y = -32

-2x + (-32) = 14
-2x = 14 + 32
2x = -46
x = -23

The important step is the first one in which you decide which letter you want to cancel. you have to the find the easiest method. Good luck

Answer 2

Elimination of x variable

-4x - 5y = - 21- - - --Equation 1
4x + 4y = 16 - - - - -Equation 2
- - - - - - - - - -

- y = - 5

-1y = -5/-1

y = 5

The answe is y = 5

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - -

Solving for x equation 1

- 4x - 5y = - 21

- 4x -5(5) = - 21

-4x - 25 = - 21

-4x - 25 + 25 = - 21 + 25

- 4x = 4

- 4x/-4 = 4/- 4

x = - 1

The answer is x = - 1

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

- 4x - 5y = - 21

- 4( - 1) - 5(5) = - 21

4 - 25 = -21

- 21 = - 21

- - - - - - - - - - - - - - - - - - - -- -

Check for equation 2

4x + 4y = 16

4(- 1) + 4(5) = 16

- 4 + 20 = 16

16 = 16

- - - - - - - - - - - - - - - - - - - - - -

The solution set is { - 1, 5 }

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Problem 2

-2x + y = 14- - - - - - -Equation 1
4x - 4y = - 36- - - - -- Equation 2

- - - - - - - - - - - - -

Substitution Method equation 1

- 2x + y = 14

-2x + y + 2x = 14 + 2x

y = 14 + 2x

Insert the y value into equation 2

- - - - - - - - - - - - - - - - - - - - - -

4x = 4y = - 36

4x - 4(14 + 2x) = - 36

4x - 56 - 8x = - 36

- 4x -56 = - 36

- 4x - 56 + 56 = - 36 + 56

- 4x = 20

-4x/-4 = 20 -4

x = - 5

The answer is x = - 5

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - - -

- 2x + y = 14

-2(- 5) + y = 14

10 + y = 14

10 + y - 10 = 14 - 10

y = 4

The answer is y = 4

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

- 2x + y = 14

- 2(- 5) + 4 = 14

10 + 4 = 14

14 = 14

- - - - - - - - - - - - - - - - - -

The solution set is { - 5, 4 }

- - - - - - s-

Answer 3

I suppose there are two questions with simultaneous equations. I'll answer assuming that.
Answer 1:
-4x - 5y = -21
4x + 4y = 16
Add the two equations.
4x - 4x + 4y - 5y = 16-21
-y = -5
y = 5
Now substitute in any one of the two equations to find 'x'
4x - 4y = 16
4x - 4*5 = 16
4x - 20 = 16
4x = 16 + 20
4x = 36
x = 36/4
x = 9

Answer 4

Do this by the Substitution Method:

-4x-5y = -21
4x+4y = 16 -4x+4x = 0 now you can solve for y.
------------------
-y = -5 divide both sides by -1
y = 5 now solve for x

4x+4(5) = 16
4x+20 = 16 subtract 20 from both sides
4x = -4 divide both sides by 4
x= -1
now plug x and y back into original equation to check

x = -1 and y = 5
-4(-1)-5(5) = -21 true
4(-1)+4(5) = 16 true

-2x+y = 14 to get a new equation multiply both sides by 4
4x-4y = -36
to ge a new equation multiply both sides by 4
in th first equation.

-8x + 4y = 56 new equation
4x - 4y = -36 4y-4y = 0 now you can solve for x.
--------------------------
-4x = 20 divide both side by -4
x = -5 now solve for y

4x - 4y = -36
4(-5)-4y = -36
-20-4y = -36 add 20 to both sides
-4y = -36 + 20
-4y = -16 divide both sides by -4
y = 4

now plug x and y back into original equation to check

x = -5 and y = 4

-2(-5)+4 = 14 true
4(-5)-4(4) = -36 true

Answer 5

1) simply add the two equations and get

-4x - 5y = -21
4x + 4y = 16 +
-------------------
0 -y =-5 => y=5 =>
.................====
4x+4*5=16=> x=(16-20)/4= -1
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2)

simply multiply equation 1 with 2 and add the equation:

2*(-2x + y) = 2*14
4x - 4y = -36.............+
----------------------------
........-2y=-8=>Y=4 =>
.....................===
x=(-36+4*4)/4= -5
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