Question

In the following exercises, solve each system by graphing.

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

Short answer

The solution of the equation is dark shaded region.

Step-by-step solution

Given information.   

Given system of equation,

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

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.

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.

Plotting the graph.