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Cxlver

Answer:

Step-by-step explanation:

[tex]\frac{1}{2}x+\frac{1}{5}y = 2 \mid 5x + 2y = c[/tex]

First let's multiply the 1st equation by 10.

[tex]5x + 2y = 20 \mid 5x + 2y = c[/tex]

So, we can see that the equations have the same coefficients and that implies  they are equal.

So the equation has no solutions for. [tex]c \in R \setminus{20}[/tex]

facundo3141592

The given system of linear equations has no solutions only when c is different than 20.

For what value of c does the system have no solution?

A system of linear equations has no solutions only when both lines are parallel.

Remember that two lines are parallel if the lines have the same slope and different y-intercept.

In this case, our lines are:

(1/2)*x + (1/5)*y = 2

5x + 2y = c

Writing both of these in the slope-intercept form, we get:

y = 5*2 - (5/2)*x

y = c/2 - (5/2)*x

So in fact, in both cases, we have the same slope.

And the only condition to not have any solution is to have:

c/2 ≠ 5*2 = 10

c/2 ≠ 10

c ≠ 10*2 = 20

c ≠ 20

So if c is any value different than 20, the system has no solution.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

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