Chapter 5, Systems of Equations and Inequalities - Section 5.2 - Systems of Linear Equations in Several Variables - 5.2 Exercises - Page 455: 41

$x=250,$ $y=500,$ $z=450$

let $x$ denote the amount of acres he grows corn let $y$ denote the amount of acres he grows wheat let $z$ denote the amount of acres he grows soybeans Thus, $x+y+z=1200$ and $45x+60y+50z=63750$. Since $y=2x$. Multiplying Equation 1 by -50 and adding it to Equation 2. $\begin{cases} -150x-50z=-60000\\ 165x+50z=63750\\ -- -- -- -- \\ 15x=3750 \end{cases}$ Thus, $x=250$. Since $y=2x, y=500$. $z=450$