-2x + 4y = 12, 5x - 2y= 10

Question

Systems help... 

Answer 1

-2x + 4y = 12 ----------(eqn 1)

5x-2y = 10 -----------(eqn 2)

Multiply eqn 2, by 2 to get equation 3.

10x-4y = 20 ---------(eqn 3)

-2x + 4y = 12 ----------(eqn 1)

Now add eqn 1 to eqn 3, to get 

8x = 32

x =32/8

x= 4

now plug in x=4, into any of the original equations to find y.

Pluging x =4 into eqn 1 gives, 

-2(4) + 4y = 12

-8 + 4y =12

4y = 12 + 8

4y = 20

y = 20/4

y = 5

therefore, X = 4  and Y = 5

Answer 2

-2x + 4y = 12

5x - 2y = 10

let's solve for x from the first equation:

-2x = 12 - 4y

divide both sides by -2

-2x/-2 = (12 - 4y) -2

x = -6 + 2y

plug in x to second equation:

5 * ( -6 + 2y) -2y = 10

-30 + 10y -2y = 10

-30 + 8y = 10

8y -30 + 30 = 10 + 30

8y = 40

8y/8 = 40/8

y = 5

let's plug in 5 to either original equations to get x:

-2x + 4 *5 = 12

-2x + 20 = 12

-2x + 20 -20 = 12 -20

-2x = -8

-2x/-2 = -8/-2

x = 4

let's plug in x=4 and y =5 to both equations:

-2 * 4 + 4 * 5 = -8 + 20 = 12            this checks out

5 * 4 - 2 * 5 = 20 - 10 = 10          this checks out.

therefore x =4, y = 5