Q 315 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing. 

$\left\{\begin{array}{l}y\ge 3x-1\\ -3x+y>-4\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the equation is dark shaded region.

Step 1: Given information.

Given system of equation, 

$\left\{\begin{array}{l}y\ge 3x-1\\ -3x+y>-4\end{array}\right.$

Step 2: Graph the system of equations.

The system of equation $y=3x-1$ 

has intercept $x=0.3,y=-1$. The boundary is solid. Origin does lies within as putting

$0\ge -1$

which holds true.

Step 3: Calculating for second equation.

For $-3x+y=4$,

the intercepts are $x=-1.3,y=4$ testing the point $(0,0)$,

we get

$0>-4$,

which is true hence, the origin is contained in it.

Step 4: Plotting the graph.