Answer:
Step-by-step explanation:
One of the two inequalities have been given as x + 2y ≤ 4, which is represented by the region below the red line drawn on graph.
Second inequality is 3x - y ≤ 2, which is represented by the region on the left of the blue line.
Solution region will be the green which is common in both the regions.
Hence all the solutions of the system of inequalities will lie in the green region.
By solving these inequalities we can get the domain and range of the solution region of this system of inequalities.
We multiply x + 2y ≤ 4 by 3 and subtract it by 3x - y ≤ 2
(3x - y) - 3(x + 2y) ≤ 2 -12
3x - y - 3x - 6y ≤ -10
-7y ≤ -10
\(y\leq \frac{10}{7}\)
Now we put the value of y in (x + 2y) ≤ 4
\(x+2(\frac{10}{7})\leq 4\)
\(x+\frac{20}{7}\leq 4\)
\(x\leq 4-\frac{20}{7}\)
\(x\leq \frac{8}{7}\)
So the domain and range of the green region will be \(x\leq \frac{8}{7}\) and \(y\leq \frac{10}{7}\).
