Solution:

In this problem, we are given a pair of linear equations in two variables x and y. We need to solve these equations by the substitution method.

Step 1: Solve one of the equations for one of the variables.

Let's solve the first equation for y:

x y - 8 ÷ 2 = x

Simplifying the left-hand side:

xy - 4 = x

Adding 4 to both sides:

xy = x + 4

Dividing both sides by x:

y = (x + 4) / x

Step 2: Substitute the expression for y into the other equation and simplify.

Using the expression we found for y, we can rewrite the second equation:

2y - 14 ÷ 3 = 3x 4 - 12 ÷ 11

Substituting (x + 4) / x for y:

2((x + 4) / x) - 14 ÷ 3 = 3x 4 - 12 ÷ 11

Simplifying:

2x + 8 ÷ 3x - 14 ÷ 3 = 3x 4 - 12 ÷ 11

Multiplying both sides by 3x:

6x^2 + 24 - 14x = 9x^2 - 36

Simplifying:

3x^2 + 14x - 24 = 0

Step 3: Solve for x using the quadratic formula.

Using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = 14, and c = -24:

x = (-14 ± sqrt(14^2 - 4(3)(-24))) / 2(3)

x = (-14 ± sqrt(400)) / 6

x = (-14 ± 20) / 6

x = 1 or x = -4

Step 4: Substitute the values of x into one of the equations to find y.

Let's use the first equation:

xy - 4 = x

If x = 1:

y - 4 = 1

y = 5

If x = -4:

y - 4 = -4

y = 0

Therefore, the solution to the pair of linear equations is (1, 5) or (-4, 0).

Conclusion:

In conclusion, we have solved the pair of linear equations by the substitution method. We first solved one of the equations for one of the variables and then substituted the expression for that variable into the other equation. We then simplified the resulting equation and solved for one of the variables using the quadratic formula. Finally, we substituted the values of the variable into one of the equations to find the value of the other variable.