Question

Solve the system of two linear inequalities graphically2x + 7y < 141x 2-3Step 1 of 3: Graph the solution set of the first linear inequalityKeypadKeyboard ShortcutsAnswerThe line will be drawn once all required data is prouded and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom PanChoose the type of boundary line:Solid (-) O Dashed (-)Enter two points on the boundary line:10Select the region you wish to be shaded:

Answer 1

The system of inequalities to be graphed is given to be:

`\begin{gathered} 2x+7y<14 \\ x\ge-3 \end{gathered}`

The first inequality can be written for y in terms of x:

`\begin{gathered} y<(14)/(7)-(2)/(7)x \\ y<2-(2)/(7)x \end{gathered}`

The following steps can be followed to plot the graph:

1) Plot the graph as you would a linear equation by getting the x and y-intercepts and graphing.

2) The type of line is dependent on the type of inequality. Strictly greater than or less than inequalities will be drawn using dotted lines.

3) The region to be shaded is dependent on the direction of the inequality. If we're considering y, we shade below the graph if y is "less than" and above if y is "greater than".

For the first inequality, the points to be plotted are gotten to be:

`\begin{gathered} At\text{ }x=0: \\ y=2 \\ At\text{ }y=0: \\ 0=2-(2)/(7)x \\ (2x)/(7)=2 \\ x=7 \end{gathered}`

Therefore, the points to be plotted are (0, 2) and (7, 0).

The line will be dotted because the inequality is strictly less than.

The region to be shaded is below the graph.

The graph is shown below: