Q 317 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing. 

$\left\{\begin{array}{l}y<\frac{3}{4}x-2\\ -3x+4y<7\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the equation is dark shaded region.  

Step 1: Given information.

Given system of equation, 

$\left\{\begin{array}{l}y<\frac{3}{4}x-2\\ -3x+4y<7\end{array}\right.$

Step 2: Graph the system of equations.

The system of equation $y=\frac{3}{4}x-2$ 

has intercept $x=2.6,y=-2$ . The boundary is solid. Origin does not lie within as putting

$0<-2$

which holds false.

Step 3: Calculating for second equation.

For $-3x+4y=7$,

the intercepts are $x=-2.1,y=1.7$ testing the point $(0,0)$,

we get

$0<7$,

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

Step 4: Plotting the graph.