Which graph represents the following system of inequalities? y < -3x+5 y < x+2 y < -1

The graph was plotted and is attached below.

Inequality is the unequal comparison of numbers or expressions.

Given the inequalities: y < -3x+5, y < x+2, y < -1

Graphing the above inequalities using the geogebra online graphing calculator.

The graph is attached below.

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The attached graph represents the system

Step-by-step explanation:

Let us describe the graph of each line

In y < -3x + 5

∵ The sign of inequality without =

∴ The line represents it must be dashed

The slope-intercept form of the inequality is y < m x + b, where m is the slope and b is the y-intercept

∵ y < -3x + 5

∴ m = -3 and b = 5

∴ The direction of the line is to the left and intersect the y-axis at (0, 5)

∴ y < -3x + 5 represented by the green line

∵ The sign of inequality is <, then the shading is under the green line

In y < x + 2

∵ The sign of inequality without =

∴ The line represents it must be dashed

∴ m = 1 and b = 2

∴ The direction of the line is to the right and intersect the y-axis at (0, 2)

∴ y < x + 2 represented by the blue line

∵ The sign of inequality is <, then the shading is under the blue line

In y < -1

∵ The sign of inequality without =

∴ The line represents it must be dashed

∴ m = 0 and b = -1

∴ The line is horizontal and intersects the y-axis at (0, -1)

∴ y < -1 represented by the red line

∵ The sign of inequality is <, then the shading is under the red line

∵ The shading of the three inequalities is under the lines

∴ The solutions of the system of inequalities lie in the common

   shaded part under the three lines

∴ The attached graph represents the system

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step-by-step explanation: