If x/y = 3/4 and 8x + 5y = 22, then find the value of x.

Concept: When two variables are linked by a ratio (x/y = a/b) and also satisfy a linear equation, express one variable in terms of the other using the ratio, then substitute into the linear equation to reduce it to a single variable.

1. From x/y = 3/4, cross-multiply to get 4x = 3y, so y = (4/3)x.

2. Substitute this into 8x + 5y = 22: 8x + 5(4/3)x = 22.

3. Combine like terms: 8x + (20/3)x = (24x + 20x)/3 = 44x/3.

4. So 44x/3 = 22, which gives 44x = 66.

5. Solving for x: x = 66/44 = 1.5.

Cross-check: y = (4/3)(1.5) = 2. Substituting back, 8(1.5) + 5(2) = 12 + 10 = 22, which matches the given equation, confirming x = 1.5.