Chapter 3 - Linear Systems - 3-2 Solving Systems Algebraically - Practice and Problem-Solving Exercises - Page 146: 27

$u = 4$, $v = 1$ or $(4, 1)$

Given: $3u + 3v = 15$ $-2u + 3v = -5$ Substract the second, $-2u + 3v = -5$, from the first, $3u + 3v = 15$ Gives: $3u + 3v - (-2u + 3v) = 15 - (-5)$ Expand: $3u + 3v + 2u - 3v = 15 + 5$ Simplify: $5u = 20$ Divide by 5: $u = 4$ Substitute back into the first equation: Gives: $3(4) + 3v = 15$ Expand: $12 + 3v = 15$ Subtract 12: $3v = 3$ Divide by 3: $v = 1$ $u = 4$, $v = 1$