what is the solution to this problem ?

Question

-4x - 2y = 6

-x + 5y = 7

Answer 1

elimination by addition Method

- 4x - 2y = 6- - - - - Equation 1
-x + 5y = 7- - - - - - Equation 2
- - - - - - - - -

Multiply equation 2 by - 4

- x + 5y = 7

- (- 4)(x) + (- 4)(5y) = - 4(7)

- (- 4x) + (- 20y) = - 28

4x - 20y = - 28

- - - - - - - - --

Elimination of x

- 4x - 2y = 6
4x - 22y= - 28
- - - - - - - - - - -

- 22y = - 22

- 22y / - 22 = - 22 / - 22

y = - 22 / - 22

y = 1

Insert the y value into equation 1
- - - - - - - - - - - -

- 4x - 2y = 6

- 4x - 2(1) = 6

- 4x - 2 = 6

- 4x - 2 + 2 = 6 + 2

- 4x = 8

- 4x / - 4 = 8 / - 4

x = - 8/4

x = - 2

Insert the x value into equation 1
- - - - - - - - - - -

Check for equation 1

- 4x - 2y = 6

- 4(- 2) - 2(1) = 6

- (- 8) - 2 = 6

8 - 2 = 6

8 = 8

- - - - - - - -

Check for equation 2

- x + 5y = 7

- (- 2) + 5(1) = 7

2 + 5 = 7

7 = 7

- - - - - - - -

Both equations balance

The solutiion set { - 2, 1 }

- - - - - - -s-

-

Answer 2

I would do this through substitution. The goal is to solve one equation for a variable and substitute that into the other. This will allow you to solve for one of the variables.

Take the second equation and solve for x:

-x + 5y = 7 so
x = 5y -7

Now substitute this into the first equation to get everything in terms of y and you get:

-4(5y-7) - 2y = 6 or
-20y + 28 - 2y = 6 or
-22y + 28 = 6 or
-22y = -22 or
y=1

Now substitiute the value of y into the second equation and you get:

-x + (5)(1) = 7 or
-x + 5 = 7 or
-x = 2 or
x = -2

Plug those values back into the 1st equation to check:

-4(-2) - (2)(1) = 6
8 - 2 = 6
6 = 6

You have the right answers.

Answer 3

i'm assuming the values of x and y are the same for both equations. You need to get one of the values by itself, either y or x... in this case x is easier to work with. This requires the law of substitution

multiply the bottom by -4 giving you

4x -20y = -28

add the two equations together which give you
(you can also subract other equations if needed)

-4x - 2y = 6 plus
4x -20y = -28
------------------------
-22y = -22

y = 1

use y = 1 in one of the equations, i'll go with the bottom one

-x + 5(1) = 7

-x + 5 = 7

-x = 2

x = -2

now we have y = 1 and x = -2
plug these numbers in the top equation to check

-4(-2) - 2(1) = 6
8 - 2 = 6

6 = 6

it works

Answer 4

multiply equation (1) by 4
-4(-x) + -4(5y) = -4(7)
becomes
4x -20y = -28
add equation 1 and 2
4x -20y = -28
-4x- 2y = 6
becomes
-22y = -22
then y=-22/-22
y =1
substitute value of y in equation 2
-x + 5(1) = 7
x = -2

Answer 5

-4x - 2y = 6----------(1)

-x + 5y = 7------------(2)

(1) - (2)*4 we get
-22y = -22 => y = 1 & plug the y value in the first equation we get -4x -2 = 6 => x = -2

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Answer 6

use addition and subtraction.

-4x -2y = 6
4x - 20y = -28
---------------------------
-22y = -22
y = 1

then substitute the value of y

-4x -2(1) = 6
-4x = 6 +2
-4x = 8
x = -2

Answer 7

x = -2 y = 1

-4x -2y = 6
4x-20y = -28

-22y = -22
y = 1
plug in
-4x -2 = 6
x = 8/-4

Answer 8

-x+5y=7
or, 5y-7=x
therefore, x=5y-7

therefore, -4(5y-7)-2y=6
or, -20y+28-2y=6
or, -22y=-22
therefore, y=1

therefore, x=5(1)-7
or, x=5-7
or, x=-2

Therefore,
x=-2 & y=1.

pls giv me 5 points!!

Answer 9

x = - .5y = -1

Multiply the bottom equation by -4 and add the two resultant equations together to solve for y. Then substitute y's value in one of the equations to solve for x.

Or multiply the top equation by 2.5 and add the two resultant equations together to solve for x. Then substitute x's value in one of the equations to solve for y.

Answer 10

x=-2
y=1