Q 316 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing. 

$\left\{\begin{array}{l}3y>x+2\\ -2x+6y>8\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the equation is dark shaded region. 

Step 1: Given information.

Given system of equation, 

$\left\{\begin{array}{l}3y>x+2\\ -2x+6y>8\end{array}\right.$

Step 2: Graph the system of equations.

The system of equation $3y=x+2$ 

has intercept $x=-2,y=0.6$. The boundary is solid. Origin does not lie within as putting

$0>2$

which holds false.

Step 3: Calculating for second equation.

For $-2x+6y=8$,

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

we get

$0>8$,

which is false hence, the origin is not contained in it.

Step 4: Plotting the graph.