I can never figure this out, but I know who to the rest...(x,y)?

Question

-x + 4y = -6
5x + 3y = -16

-5x + y = 23
-x + y = 3

x - 2y = 12
-x + 5y = -24

Thank you soo much

Answer 1

There are 2 ways.
1st - Substitution
In the first equation solve for x.
x=4y+6
In the second equation substitute 4y+6 for x.
5(4y+6)+3y = -16
23y=-46
y=-2 No use -2 for y in either equation and ckeck the other
with x and y. Using the first -x+4(-2)=-6
so x=-2
Checking 5(-2)+3(-2)=-10-6=-16 OK

2nd by adding (or subtracting) simultanious equations

Multiply the first thru by 5
-5x + 20y=-20 and add this equation to the second.
This gives 23y=-46 so y=-2 and you can do the rest.

Try the last 2 yourself befor reading on so you get the
mental exercise of doing. Reading the answer is not
the same as doing it
2nd pair of equations - Subtract the second equation from the
first to get rid of the y. -5x+x=23-3 ==> -4x=20
x=-5. -(-5)+y=3 ==> y=-2
Checking: -5(-5)+(-2)=25-2=23 OK

3rd pair
Add equations to eliminate x
-2y+5y=36 ==> 3y=-12 ==> y=-4
x-2(-4)=12 ==> x=4
Checking: -4 +5(-4)=-24 OK

Answer 2

I wil answer the first one to demonstrate:

-x + 4y = -6
now multiply this by 5
-5x + 20y = -30
and add to the second equation
(-5x)+5x+(20y)+3y = (-30)+-16
so 23y = -46, and y = -2. substituting that in the first equation, we get
-x+4*(-2) = -6 ;
-x = 2, x = 2

Solving the other two similarly, we get x=-5, y = -2
and x=4, y = -4

Steve

Answer 3

x=4y+6
5(4y+6)+3y=-16
20y+30+3y=-16
23y=-46
y=-2
x=4y+6
x=4(-2)+6
x=-2

x=y-3
-5(y-3)+y=23
-5y+15+y=23
-4y=8
y=-2

-x+y=3
-x-2=3
x=-5

you can do the last one now

Answer 4

you stuffin ur head wid all that fancy letter math thats why you cant never figur it out!!