Make Your Move.

Question

Lin and Priya were working on solving this system of equations.

Lin's first move is to multiply the first equation by 3. 

Priya's first move is to multiply the second equation by 2.

1. Explain why either move creates a new equation with the same solutions as the original equation.
2. Whose first move would you choose to do to solve the system? Explain your reasoning.

Answer 1

multiplies first equation by 3 so as

to clear away the fractions:

x + 6y = 12

vs

x + y = -3

subtracts: 5y = 15

y = 3 ---> x = -6

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multiplies 2nd equation by 2=6/3:

then

1/3 x + 2y = 4

6/3 x + 2y = -6

subtracts:

5/3 x = -10

x = (-10)(3/5) = -6

then (1/3)(-6) + 2y = 4

-2 + 2y = 4

2y = 6

y = 3