Which system of inequalities is shown in the graph

The system of inequalities shown in the graph is x ≤ 4 and y > 1 ⇒ C

Step-by-step explanation:

In the given figure, there are 2 lines, let us find the equations of them, then write the inequalities which represent the shaded areas

∵ The purple line is a vertical line

∵ It is cross the x-axis at the point (4, 0)

→ By using the first rule above

∴ The equation of the purple line is x = 4

∵ The purple line is solid and the shaded area left the line

∴ The sign inequality is ≤

∴ The inequality of the purple area is x ≤ 4

∵ The blue line is a horizontal line

∵ It is cross the y-axis at the point (0, 1)

→ By using the second rule above

∴ The equation of the blue line is y = 1

∵ The blue line is dashed and the shaded area above the line

∴ The sign inequality is >

∴ The inequality of the blue area is y > 1

∴ The system of inequalities shown in the graph is x ≤ 4 and y > 1

∴ The value of x is - 1

We have,

2x + 30 = - 4(5x - 2)

Substituting the value of x,

2(- 1) + 30 = - 4{5(- 1) - 2}

- 2 + 30 = - 4 (- 5 - 2)

28 = - 4(- 7)

28 = 28

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