Chapter 3 Linear Systems and Matrices - 3.2 Solve Linear Systems Algebraically - 3.2 Exercises - Skill Practice - Page 165: 49

$x=7,y=1$

After multiplying the first equation by $6$ we get: $3(x-1)+2(y+2)=24\\3x-3+2y+4=24\\3x+2y=23$ If we multiply the second equation by $-3$ we get: $-3x+6y=-15$. Adding this to the modified version of the first equation we get: $8y=8\\y=1$. Then $3x+2(1)=23\\3x=21\\x=7$