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1. the following proof shows an equivalent system of equations created from another system of equations. fill in the missing reason in the proof.

statements reasons

2x + 2y = 14

−x + y = 5 given

2x + 2y = 14

y = x + 5 ?

multiplication property of equality

addition property of equality

division property of equality

subtraction property of equality

2.explain how system 1 becomes equivalent to system 2.

system 1:

lx + my = n

ax + by = c

system 2:

(l − a)x + (m − b)y = n − c

lx + my = n

the first equation in system 2 is the sum of the equations in system 1. the second equation in system 2 is the first equation in system 1.

the first equation in system 1 is the difference of the equations in system 2. the second equation in system 1 is the first equation in system 2.

the first equation in system 2 is the difference of the equations in system 1. the second equation in system 2 is the first equation in system 1.

the first equation in system 1 is the sum of the equations in system 2. the second equation in system 1 is the first equation in system 2.

3.

create an equivalent system of equations using the sum of the system and the first equation.

−3x + y = 12

x + 3y = 6

−3x + y = 12

−2x + 4y = 18

−3x + y = 12

−3x + 4y = 18

−3x + y = 12

x + 4y = 18

−3x + y = 12

−2x + 4y = 6

4.choose a system of equations with the same solution as the following system:

6x + 2y = −6

3x − 4y = −18

8x + 4y = −4

17x + 2y = −28

12x + 4y = 12

21x + 2y = −36

6x + 8y = −36

15x + 6y = −60

6x + y = 15

15x − y = −9