Answer
$ x+y \leq 3$
$4x+y \leq 6 $
.
Work Step by Step
First sentence: $\quad x+y \leq 3 \quad\Rightarrow y \leq -x+3$
Second sentence: $\quad 4x+y \leq 6 \quad \Rightarrow y \leq -4x+6$
Both inequalities have the $ \leq$ inequality sign, so both border lines will be solid.
1st inequality:
Graph $y=-x+3:$
y intercept=$3$, and for x=3, y=0 .
Draw the line through (0,3) and (3, 0)
Test point: (0,0). Is $0 \leq -(0)+3\quad ?$
Yes. shade the region containing (0,0).
2nd inequality:
Graph $y=-4x+6$
y intercept=$6$, and for x=$2$, y=$-2$ .
Draw the line through (0,$6$) and ($2,\ -2$)
Test point: (0,0). Is $0 \leq -4(0)+6\quad ?$
Yes. shade the region containing (0,0).
The solution set is the region with both shadings.
(grey on the screenshot)
