This document contains Mrs. Crespo's solutions to homework problems 21, 37, 39, 45, and 46 from Lesson 2.5 in Algebra II. The solutions involve solving systems of equations by substitution. For each problem, Mrs. Crespo lets one variable equal an expression containing the other variable, substitutes this into the second equation to solve for the substituted variable, then substitutes back into the original equation to solve for the remaining variable.

1. Mrs. Crespo’s Solutions on Lesson 2.5 HW page 109 21, 37, 39, 45, 46 Algebra II 2012-2013
#21
√ √
(Subtract √ from both sides.)
√ √
( √ ) ( √ )
( ) ( ) ( )( √ ) ( √ )
√ ( )
√
√
√
√
√
√
( ) ( √ )
( )
( )( )
double root

2. Mrs. Crespo’s Solutions on Lesson 2.5 HW page 109 21, 37, 39, 45, 46 Algebra II 2012-2013
#37
( ) ( )
Let
Substitute and solve for z.
( ) ( )
Q.F.
( ) √( ) ( )( )
( )
√
√
Bring back and solve for y.
√
√
√ √ √
√ √
√ √
√
√
√
√ √
√ √

3. Mrs. Crespo’s Solutions on Lesson 2.5 HW page 109 21, 37, 39, 45, 46 Algebra II 2012-2013
#39
( ) ( )
Let
Substitute and solve for z.
( ) ( )
Q.F.
( ) √( ) ( )( )
( )
√ )
√
Bring back and solve for y.
( ) ( )
( )
√ √

4. Mrs. Crespo’s Solutions on Lesson 2.5 HW page 109 21, 37, 39, 45, 46 Algebra II 2012-2013
( ) ( )
( )
√ √
#45
( ) ( )
Let
Substitute and solve for z.
( )( )
Bring back and solve for y.
( ) ( ) ( ) ( )
( ) ( )

5. Mrs. Crespo’s Solutions on Lesson 2.5 HW page 109 21, 37, 39, 45, 46 Algebra II 2012-2013
#46
( ) ( )
Let
Substitute and solve for z.
( ) ( )
( )( )
Bring back and solve for y.
( ) ( ) ( ) ( )
( ) ( )