Question

Graph the system of linear inequalities and shade in the solution set. If there are no solutions, graph the corresponding lines and do not shade in any region. X - y > 3 Y < - 2x + 5

Answer 1

Step-by-step explanation:

Given the below system of linear inequalities;

`\begin{gathered} x-y>3 \\ y<-2x+5 \end{gathered}`

A slope-intercept equation of a line is generally given as;

`y=mx+b`

where m = slope of the line

b = y-intercept of the line

Let's go ahead and represent the first inequality in slope-intercept form by subtracting x from both sides and multiplying both sides by -1 as seen below;

[tex]\begin{gathered} x-x-y>-x+3 \\ -y>-x+3 \\ -1(-y)>-1(-x+3) \\ yIf we now compare y < x - 3 with the slope-intercept equation, we'll see that the slope(m) of the line is 1 and the y-intercept(b) of the line is -3. Since we have only an inequality sign without an equality sign, the line will be a dashed line. We have a less than sign, therefore the part of the graph of the part to be shaded will be below the line as seen below;

If we compare y < -2x + 5 with the slope-intercept equation, we'll see that the slope(m) of the line is -2 and the y-intercept(b) of the line is 5. Since we have only an inequality sign without an equality sign, the line will be a dashed line. The part of the line to be shaded will be below the line since we also have a less than sign as seen below;

See below the graph of the system of linear inequalities and shaded solution set;

Note that the solution of the system of inequalities is the area where the 2 shadings intersect. We can see from the above that this part is shaded green which represents the solution set of the system of inequalities.