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)

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)