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Answer:

The solution of the system shown is (2k, k)

Step-by-step explanation:

We have a systems of two equations:

First equation: x+y = 3k

Second equation: x - y = k

From the second equation we get that: x = k + y (1)

Substituting (1) in the first equation we get:

k + y + y = 3k

Solving for y:

2y = 2k ⇒ y = k.

Then, let's find the value of "x" using equation (1):

x = k + y ⇒ x = k + k = 2k

The solution of the system shown is: (2k, k)

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ANSWER

The solution of the system shown is (2k,k)

EXPLANATION

The given system of equations are:

First equation:

[tex]x + y = 3k[/tex]

Second equation:

[tex]x - y = k[/tex]

We consider this to be a simulation equation in x and y, and then treat k as a constant.

Let us eliminate y, by adding the two equations:

[tex]x + x = 3k + k[/tex]

This implies that:

[tex]2x = 4k[/tex]

[tex]x = 2k[/tex]

Let us now substitute x=2k into any of the equations, say , the second equation.

[tex]2k - y = k[/tex]

Group similar terms.

[tex] - y = k - 2k[/tex]

[tex] - y = - k[/tex]

[tex]y = k[/tex]

The solution is therefore (2k,k)

The last choice is correct.

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