Having trouble solving

Question

6x - 3y =4; 6x + 3y =7 using the elimination method

Answer 1

6x - 3y = 4

6x + 3y = 7

adds:

12x = 11

x = 11/12

1st equation:

6(11/12) - 3y = 4

11/2 - 3y = 4

11 - 6y = 8

-6y = 8 - 11

-6y = -3

y = -3/-6 = 1/2

unofficial solution (11/12, 1/2)

2nd equation:

6x + 3y = 6(11/12) + 3(1/2) =

66/12 + 3/2 =

66/12 + 18/12 =

84/12 =

7

official solution ( 11/12, 1/2)

yes it checks

Answer 2

To use the elimination method, modify the equations as necessary to get them into standard form (Ax + By = C) but in this case, they already are in that form. Now place them over the top of one another like this:

And look for a way to adjust either equation as necessary so that when added together, one of the variables will be eliminated. Notice that in this case, you do not have to adjust anything. If you add them together the way they are, the "y" will be eliminated because "-3y" and "3y" add to zero. So, add the two equations together to get:

12x + 0 = 11

12x = 11

x = 11/12

Now, plug the value of "x" into one of the equation (doesn't matter which one). I'll pick:

6x - 3y = 4 so:

6(11/12) - 3y = 4

11/2 - 3y = 8/2

-3y = -3/2

y = 1/2

So the solution is x = 11/12 and y = 1/2 or the point (11/12, 1/2)