How To Solve The Following System Of Equations Using Either Substitution Or Elimination Method?

6x - 5y = 7    (given equations)
4x - 6y = 7

Multiply the first equation by 2 and the second equation by 3
12x - 10y = 14
12x - 18y = 21

Subtract the second of these from the first
(12x - 10y) - (12x - 18y) = -10y - (-18y) = 14 - 21
8y = -7
y = -7/8    (divide both sides by 8)

Substitute this result into the first of the given equations
6x - 5(-7/8) = 7
6x + 35/8 = 7    (perform the arithmetic)
6x = 7 - 35/8 = (56-35)/8 = 21/8    (subtract 35/8 from both sides)
x = (21/8)/6 = 7/16    (divide both sides by 6)

Check
Since we used the first equation to derive the result, we'll check in the second equation.
4(7/16) - 6(-7/8) = 7
7/4 + 21/4 = 7
28/4 = 7    (yes)