Chapter 3 - Linear Systems - 3-2 Solving Systems Algebraically - Practice and Problem-Solving Exercises - Page 146: 30

$r = 2$, $s = -1$ or $(2, -1)$

Given: $2r + s = 3$ $4r - s = 9$ Add the equations: Gives: $2r + s + (4r - s) = 3 + (9)$ Expand: $2r + 4r + s - s = 3 + 9$ Simplify: $6r = 12$ Divide both sides by $6$: $r = 2$ Substitute $r = 2$ into the first equation: $2(2) + s = 3$ Expand: $4 + s = 3$ Subtract $4$ to both sides: $s = -1$ $r = 2$, $s = -1$