Question

X + y = 3k x - y = k The solution of the system shown is _____. (0, 2k) (2k, 0) (2k, k)

Answer 1

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

EXPLANATION

The given system of equations are:

First equation:

`x + y = 3k`

Second equation:

`x - y = k`

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:

`x + x = 3k + k`

This implies that:

`2x = 4k`

`x = 2k`

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

`2k - y = k`

Group similar terms.

`- y = k - 2k`

`- y = - k`

`y = k`

The solution is therefore (2k,k)

The last choice is correct.

Answer 2

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

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)