5x+6y=7 2x+3y=4

Let's look at this again

5x+6y=7   (1)

2x+3y=4   (2)

Multiply (2) by -2 and add it to the first equation.....this produces

x  = -1

And substituting this into (2) to find y, we have

2(-1) + 3y  = 4

-2 + 3y  = 4      add 2 to both sides

3y  = 6               divide by 3 on both sides

y = 2

So.....the solution is (x,y) = (-1 , 2)

X = 1

Y = 2/6