Question

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!

Answer 1

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

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

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

`3(3y+19)-4y=32\\ 9y+57-4y=32\\ 5y+57=32\\ 5y=-25\\ y=-5`

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

`-2x+6(-5)=-38\\ -2x-30=-38\\ -2x=-8\\ x=4\\ \\ 3x-4(-5)=32\\ 3x+20=32\\ 3x=12\\ x=4`

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

Answer 2

-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).