Question

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

Answer 1

Answer:

we can conclude two things that:

1. If we multiple the two sides of any given equation by the same factor, we would get an equivalent equation, which will have the same solution as the original solution.
2. Either person's move will work. Lin's move eliminated the x variable, while Priya's eliminated y variable, but in the end the solution was same.

Step-by-step explanation:

Why either move creates a new equation with the same solutions as the original equation?

If we multiple the two sides of any given equation by the same factor, we would get an equivalent equation, which will have the same solution as the original solution.

When we multiple the two sides of any given equation by the same number, it would keep the two sides of that particular equation equal. So, whatever the  the solution the first equation may get, will still work for the second equation.

Determining Lin's first move i.e. to multiply the first equation by 3.

Let us consider the equation

x/3 + 2y = 4      .....[1]

x + y = -3           .....[2]

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

3(x/3 + 2y) = 3(4 )

x + 6y = 12         .....[3]

Now subtract the Equation [2] from Equation [3]

x + 6y - x - y = 12 - (-3)

5y = 15

y = 3

Putting y = 3 in [2]

x + (3) = -3

x = -6

So, x = -6 and y = 3

Determining Priya's first move i.e. to multiply the Second equation by 2.

Let us consider the equation

x/3 + 2y = 4      .....[1]

x + y = -3           .....[2]

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

2(x + y) = 2(-3)          

2x + 2y = -6           .....[3]

Now subtract the Equation [2] from [1]

x/3 + 2y - 2x - 2y= 4 - (-6)

x/3 - 2x = 10

x - 6x = 30

x = -6

Putting x = -6 in Equation [2]

x + y = -3

-6 + y = -3

y = 3

So, x = -6 and y = 3

So, from the entire analysis, we can conclude two things that:

1. If we multiple the two sides of any given equation by the same factor, we would get an equivalent equation, which will have the same solution as the original solution.
2. Either person's move will work. Lin's move eliminated the x variable, while Priya's eliminated y variable, but in the end the solution was same.

Keywords: system of equation, solution, equation

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