Final answer:
To eliminate y from the system of equations using linear combinations, we should multiply the second equation by the factor -3/2. This allows the y terms to have equal magnitudes but opposite signs, leading to their cancellation when the equations are combined.
Step-by-step explanation:
To eliminate y and solve the system of equations through linear combinations, we first observe the coefficients of y in both equations:
1st equation: \(\frac{3}{4}y\)
2nd equation: \(\frac{1}{2}y\)
To find a common multiple, we can multiply the second equation by a factor that will make the coefficient of y in the second equation equal in magnitude but opposite in sign to the coefficient of y in the first equation. This factor is \(-\frac{3}{4}\) times 2 (which is the denominator of \(\frac{1}{2}\) to make it equal to \(\frac{3}{4}\)).
The calculation would be: \(-\frac{3}{4} \times 2 = -\frac{3}{2}\), so we obtain:
\(-\frac{3}{2} \times 2x + -\frac{3}{2} \times \frac{1}{2}y = -\frac{3}{2} \times 9\)
After applying this factor, the y terms will cancel when we add or subtract the two equations, allowing us to solve for x. Therefore, the correct answer is C. -3/2.