Which part should you shade for C to be a solution?
y $>$ - 3x+4 y $<$ 2x+1 or y $>$ - 3x+4 y $≤$ 2x+1
Practice makes perfect
In order for C to be a solution to the system of inequalities, we have to shade the region to the right of both inequalities. Let's do that and see what happens.
Let's isolate the shading where both inequalities apply.
At the moment the shaded area includes both B and C as solutions, as B is on the boundary line of y=- 3x+4. To exclude B we have to use either > or < for this boundary line. But which one? Let's find out by substituting C(4,5).
y - 3x+4
This should form a true statement.
In order to form a true statement we need to use > to complete the inequality.
y>- 3x+4
For y=2x+1 there are no solutions on its boundary line. Therefore, we can either keep the line solid or dashed. Let's find out which way the inequality symbol should point by substituting point C.
y 2x+1
Again, this should form a true statement when substituted.
For the second inequality we can either use < or ≤ for it to be true. Finally, let's summarize the inequalities.
y $>$ - 3x+4 y $<$ 2x+1 or y $>$ - 3x+4 y $≤$ 2x+1
