Chapter 8 - Section 8.1 - Systems of Linear Equations: Substitution and Elimination - 8.1 Assess Your Understanding - Page 555: 25

$x=\frac{1}{3}$ $y=-\frac{1}{6}$ $(\frac{1}{3},-\frac{1}{6})$

$3x - 6y = 2$ $(1)$ $5x+4y=1$ $(2)$ Multiply Equation $(1)$ by 2 and Equation $(2)$ by 3 $6x-12y=4$ $(1)$ $15x+12y=3$ $(2)$ Add Equation $(1)$ and Equation $(2)$ $21x = 7$ $x= \frac{7}{21} = \frac{1}{3}$ Substitute into Equation $(1)$ $3(\frac{1}{3}) - 6y =2$ $1-6y=2$ $-6y=1$ $y=-\frac{1}{6}$