How To Solve This Equation 3x+6y=6 2x-3y=4?

To solve this sysetm of equations, line the equations up

3x+6y=6
2x-3y=4

Multiple each term in the second equation by 2, so it is
4x-6y=8

Now line them up again.
3x+6y=6
4x-6y=8

Add, so the sum is
7x=14
x=2

Substitute the x=2 into one of the original equations.
3x+6y=6
3*2+6y=6
6+6y=6
6y=0
y=0

The solution is (2,0)

This system of equations can be solved by elimination. Add twice the second equation to the first.
  (3x + 6y) + 2(2x - 3y) = (6) + 2(4)
  3x + 6y + 4x - 6y = 6 + 8    (use the distributive property to eliminate parentheses)
  7x = 14    (collect terms)
  x = 2    (divide by 7)
Substituting this into the first equation, we get
  3(2) + 6y = 6
  6y = 0    (subtract 6 from both sides)
  y = 0    (divide by 6)

The solution is (x, y) = (2, 0).