Chapter 8 - Section 8.1 - Systems of Linear Equations: Substitution and Elimination - 8.1 Assess Your Understanding - Page 557: 71

$y=75$ mg $x=50$ mg

Liquid 1 = $20$% vitamin C and $30$% vitamin D Liquid 2 = $40$% vitamin C and $20$% vitamin D Liquid 1 = $x$ mg Liquid 2 = $y$ mg $[^{0.2}_{0.3}⠀^{0.4}_{0.2}] [^x_y] = [^{40}_{30}]$ $[^{0.2}_{0}⠀^{0.4}_{-0.4}] [^x_y] = [^{40}_{-30}]$ $R_{2} = R_{2} - \frac{3}{2}R_{1}$ $y = \frac{-30}{-0.4} = 75$ mg $x = \frac{40-0.4y}{0.2} = 50$ mg