12x+5y==13

-24x-5y=-11

-2x+4y=32

-5x-10y=-20

12x+12y=36

-8x-8y=-8

solve and explain

1. 12x + 5y = 13

-24x - 5y = - 11

First Add these equations to cancel out the y value so we can find the x value.

(12x + 5y = 13) + (-24x - 5y = - 11)

= - 12x + 0y = 2

Now we are left with the equation - 12x = 2

Next divide both sides by - 12 and x = - 1/6

Now plug x into any of the original two equations to find the y-value.

12 (-1/6) + 5y = 13

-2 + 5y = 13

5y = 15

y = 3

or

-24 (-1/6) - 5y = - 11

4 - 5y = - 11

-5y = - 15

y = 3

Sp, x = - 1/6 and y = 3

2.-2x + 4y = 32

-5x - 10y = - 20

First, lets simplify both of the equations.

(-2x + 4y = 32) / - 2 = x - 2y = - 16

(-5x - 10y = - 20) / - 5 = x + 2y = 4

Now we have the two equations:

x - 2y = - 16

x + 2y = 4

Subtract the equations from each other to cancel out the 'x'.

(x - 2y = - 16) - (x + 2y = 4)

= - 4y = - 20

-4y = - 20

Divide by - 4

y = 5

Now plug 5 in for y in the equations:

x - 2y = - 16

x + 2y = 4

x - 10 = - 16

x = - 6

x + 10 = 4

x = - 6

So, y = 5, and x = - 6

3. 12x + 12y = 36

-8x - 8y = - 8

Lets also simplify the equations.

(12x + 12y = 36) / 12 = x + y = 3

(-8x - 8y = - 8) / - 8 = x - y = 1

Right off the bat you can say that x = 2 and y = 1.

2 + 1 = 3

2 - 1 = 1

But mathematically:

Subtract both equations

(x + y = 3) - (x - y = 1)

= 2y = 2

2y = 2

y = 1

x + 1 = 3

x = 2

x - 1 = 1

x = 2

So x = 2 and y = 1;

12x+5y=13 is y=13/5-12/5x

-24y-5y=-11 is y=-11/-5 + (24/-5) x

-2x+4y=32 is y=32/4+2/4x

-5x-10y=-20 is y = - 20/-10 + (5/-10) x

12x+12y=36 is y=36/12-12/12x

-8x-8y=-8 is y=-8/-8 + (8/-8) x