Chapter 8 - Section 8.1 - Systems of Linear Equations: Substitution and Elimination - 8.1 Assess Your Understanding - Page 555: 35

$x=\frac{3}{2}$ $y=1$ $(\frac{3}{2},1)$

$2x+3y=6$ $(1)$ $x-y=\frac{1}{2}$ $(2)$ Multiply Equation $(2)$ by 2 $2x+3y=6$ $(1)$ $2x-2y=1$ $(2)$ Subtract Equation $(1)$ from Equation $(2)$ $5y=5$ $y=1$ Substitute back to Equation $(2)$ $x-1 = \frac{1}{2}$ $x=\frac{1}{2} + 1$ $x= \frac{3}{2}$