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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.