Solve the system by the method of substitution. (If there is no solution, enter NO SOLUTION.)\frac{1}{2}x + \frac{3}{4}y = 14 \ \frac{3}{2}x – y = 16

We want to solve for one variable in terms of the other in one of the equations, and then substitute that expression into the other equation. Let's solve the second equation for y: {eq}begin{align*} frac{3}{2}x - y &= 16 \ -y &= -frac{3}{2}x + 16 \ y &= \frac{3}{2}x - 16 end{align*} {/eq} Now we substitute this expression for y into the first equation: {eq}begin{align*} frac{1}{2}x + \frac{3}{4}y &= 14 \ frac{1}{2}x + \frac{3}{4}\frac{3}{2}x - 16) &= 14 \ frac{1}{2}x + \frac{9}{8}x - 12 &= 14 \ frac{13}{8}x &= 26 \ x &= 16 end{align*} {/eq} Now that we know x is 16, we can substitute this value back into the equation we solved for y: {eq}begin{align*} y &= \frac{3}{2}x - 16 \ y &= \frac{3}{2}(16) - 16 \ y &= 8 end{align*} {/eq} Therefore, the solution is {eq}(x,y) = (16,8) {/eq}.