Question

A graph and the system of inequalities are shown above. Which region of the graph could represent the solution for the system of in equations?

$y>x$

$3y\le -4x+6$

• A. $A$
• B. $B$
• C. $C$
• D. $D$

Answer 1

The correct option is D $D$

given $y>x$

and $3y\le -4x+6$

first, draw the graph for equations $y=x$ and $3y=-4x+6$

$y=x$ is the line which passes through the origin as shown in the above fig

Hence, $y>x$ includes the above region of the line.

similarly, for $3y=-4x+6$

substitute y=0 we get, $-4x+6=0⟹x=1.5$

substitute x=0 we get, $3y=6⟹y=2$

therefore, $3y=-4x+6$ line passes through (1.5,0) and (0,2) as shown in fig.

Hence, $3y\le -4x+6$ includes the region below the line.

the intersection region is the D region as shown in above figure.