To solve this, we will use the method of substitution-

2x + 3y = 9 …(1)

8x – 2y = 5 …(2)

Step 1: Solve equation (1) for x in terms of y:

2x = 9 – 3y

x = (9 – 3y) / 2

Step 2: Substitute x in equation (2) with the expression we obtained in step 1:

8((9 – 3y) / 2) – 2y = 5

Simplifying further:

4(9 – 3y) – 2y = 5

36 – 12y – 2y = 5

36 – 14y = 5

-14y = 5 – 36

-14y = -31

y = (-31) / (-14)

y = 31/14

y ≈ 2.2143

Step 3: Substitute the value of y back into equation (1) to find x:

2x + 3(2.2143) = 9

2x + 6.6429 = 9

2x = 9 – 6.6429

2x ≈ 2.3571

x ≈ 1.1786

Therefore, the solution to the system of equations is approximately x ≈ 1.1786 and y ≈ 2.2143.