Solve the following system with substitution and elimination

Question

2x - 4y = 2

3x + 6y = 1

Answer 1

First of all the 1st equation can be divided by 2:

x - 2y = 1 ---> x = 2y+1

Substitution:

3(2y+1) + 6y = 1

6y + 3 + 6y = 1

12y + 3 = 1

12y = -2

y = -2/12 = -1/6

then x = 2(-1/6)+1

= -1/3 + 1

= 2/3

the solution is (2/3, -1/6)

check: 2x - 4y = 2(2/3) - 4(-1/6)

= 4/3 + 4/6

= 8/6 + 4/6

= 12/6 = 2 , so the first equation checks;

3x + 6y = 3(2/3) + 6(-1/6)

= 2 + -1 = 1, so the 2nd equation checks;

Now for the elimination:

2x - 4y = 2

3x + 6y = 1

To eliminate the X:

3(2x-4y = 2)

-2(3x+6y = 1)

6x - 12y = 6

-6x + -12y = -2

-24 y = 4

y = -4/24 = -1/6

2x - 4(-1/6) = 2

2x + 4/6 = 2

2x + 2/3 = 2

6x + 2 = 6

6x = 4

x = 4/6 = 2/3

solution is (x=2/3, y=-1/6)

to eliminate the Y:

3(2x - 4y = 2)

2(3x + 6y = 1)

6x - 12y = 6

6x + 12y = 2

12x = 8

x = 8/12 = 2/3

3(2/3) + 6y = 1

2 + 6y = 1

6y = -1

y = -1/6