Respuesta :

chrysanthemum

-2x + 6y = -38

3x - 4y = 32

To solve by elimination, multiply the top equation by 3 and the bottom equation by 2.

3(-2x + 6y = -38) --> -6x + 18y = -114

2(3x - 4y = 32) --> 6x - 8y = 64

Add the equations.

-6x + 18y = -114

6x - 8y = 64

+_____________

0 + 10y = -50

10y = -50

y = -5

Substitute -5 for y into one of the original equations to find x.

3x - 4y = 32

3x - 4(-5) = 32

3x + 20 = 32

3x = 12

x = 4

Check work by plugging the x- and y-values into both of the original equations.

-2x + 6y = -38

-2(4) + 6(-5) = -38

-8 - 30 = 38

38 = 38


3x - 4y = 32

3(4) - 4(-5) = 32

12 + 20 = 32

32 = 32

Answer:

x = 4 and y = -5; (4, -5).

GoddessofDork

I'll be using the substitution method, so firstly, subtract 6y on both sides of the first equation: [tex] -2x=-6y-38 [/tex]

Next, divide by -2 on both sides of the first equation: [tex] x=3y+19 [/tex]

Now substitute x in the second equation with (3y + 19) to solve for y as such:

[tex] 3(3y+19)-4y=32\\ 9y+57-4y=32\\ 5y+57=32\\ 5y=-25\\ y=-5 [/tex]

Now that we have the value of y, substitute it in either equation to solve for x:

[tex] -2x+6(-5)=-38\\ -2x-30=-38\\ -2x=-8\\ x=4\\ \\ 3x-4(-5)=32\\ 3x+20=32\\ 3x=12\\ x=4 [/tex]

In short, your solution is (4, -5), or the first option.

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