I've included my work with the answers I got, below. I'm probably not following the method to a T, but I'm not terribly worried about that. The answers aren't in the back of the book, but I modeled the circuit on a simulator and its results agreed with mine.

V1-V(R1)-V(R3)=0

V2-V(R3)-V(R2)=0

__V2-V(R3)-V(R2)=0__

15-15*I3-10*I2=0

15-15*(I1+I2)-10*I2=0

15-15*I1-15*I2-10*I2=0

15-15*I1-25*I2=0

15*I1+25*I2=15

I2=(15-15*I1)/25=3/5-3/5*I1

__V1-V(R1)-V(R3)=0__

10-10*I1-15*I3=0

10-10*I1-15*(I1+I2)=0

10-10*I1-15*I1-15*I2=0

10-25*I1-15*I2=0

25*I1+15*I2=10 -----------------------------> 25*1/16+15*I2=10

25*I1+15*(3/5-3/5*I1)=10..................... 10-25/16=15*I2

25*I1+45/5-45/5*I1)=10........................ 160/16-25/16=15*I2

25*I1+9-9*I1=10................................... 135/16=15*I2

16*I1=1.................................................

**I2=9/16 A**

I1=1/16 A

I1=1/16 A

__V1-V(R1)-V(R3)=0__

10-10*1/16-15*I3=0

10-10/16=15*I3

160/16-10/16=15*I3

(150/16)/15=I3

**I3=10/16 A**

**V(R1)=**10*1/16=

**10/16 V=0.625 V**

V(R2)=10*9/16=90/16

V(R2)=

**=5.625 V**

V(R3)=15*10/16=150/16

V(R3)=

**=**

**9.375 V**Number 11 says to use KVL to prove that the sum of the voltages is zero in each of the three closed loops. For the left loop, going counter-clockwise from the negative terminal of V1, it says the answer is -10 V + 16.875 V - 15 V + 8.125 V = 0; for the right loop, counter-clockwise from the positive terminal of V2, it says the answer is 15 V - 16.875 V + 1.875 V = 0; for the outside loop, going counter-clockwise from the negative terminal of V1, it gives -10 V + 1.875 V + 8.125 V = 0.

Honestly, I have no idea what to do with the left loop, with its two voltage sources, but for the right loop, I would think 15 V - 15*10/16 - 10*9/16 = 0 (or 15 V - 9.375 V - 5.625 V = 0) should be the answer. For the outside loop, I would think - 10 V + 10*1/16 + 15*10/16 = 0 (or 10 V + 0.625 V + 9.375 V = 0) should be the answer. As I mentioned, these are not the answers the book gives. Could someone please help me understand where I am going wrong?

Number 12 involves analyzing the same circuit using the method of mesh currents, but I'll try to work through that one again before asking.

Thank you!