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A system of linear inequalities is shown below:

y − x > 0
y − 1 > 0

Which of the following graphs best represents the solution set to this system of linear inequalities?

A system of linear inequalities is shown below y x gt 0 y 1 gt 0 Which of the following graphs best represents the solution set to this system of linear inequal class=
A system of linear inequalities is shown below y x gt 0 y 1 gt 0 Which of the following graphs best represents the solution set to this system of linear inequal class=
A system of linear inequalities is shown below y x gt 0 y 1 gt 0 Which of the following graphs best represents the solution set to this system of linear inequal class=
A system of linear inequalities is shown below y x gt 0 y 1 gt 0 Which of the following graphs best represents the solution set to this system of linear inequal class=

Respuesta :

Answer: Graph D represents the given inequality.

Explanation: Since, given inequalities, y − x > 0  ------(1)

y − 1 > 0    -----(2)

And, the intersection point of line (1) and (2) is (1,1)

Since, for the line , y-x>0, if x=0 and y=0 then 0>0 (not true)

therefore, the area of the line will not comprise the point (0,0)

Again, For inequality (2) -1>0(not true) at (0,0) therefore, the area of inequality (2) also does not consist of origin.

Thus, after making the common area of inequalities (1) and (2) we found only graph four is the correct graph for the given system.

Note: In graph (1) The system does not contains the common area.So, it can not be the graph of the system.

In graph (2) the area of the system is missing in second quadrant.So it can not be the graph of the system.

In graph (3)  the area of the system is missing in first quadrant.So it can not be the graph of the system.

Ver imagen parmesanchilliwack

Answer:

A system of linear inequalities is shown below:

y − x > 0---------(1)

y − 1 > 0---------(2)

  • Firstly we will graph the inequality (1) as:

we will make a dashed line,

y-x=0

y=x

and the shaded region will be above the line since this inequality could also be represented as:

y>x

so, the points above the line have y-value greater than x values.

  • Now we will plot the graph of the line,

y-1=0

i.e. y=1

The line will be dashed as the inequality is strict also the line is horizontal and the shaded region will be above the line as the inequality is:

y>1

so, it does not satisfy zero point test.

i.e. on putting (0,0) in the inequality the inequality holds false.

The graph is attached to the answer.

Ver imagen virtuematane

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