Answers
(0,0) is a solution
(2,3) is NOT a solution
Solution points are in the shaded region.
In this particular case, points on the boundary are also part of the solution set.
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Step-by-step explanation
Plug the coordinates of (0,0) into the inequality. Then simplify.
4x + 7y ≤ 26
4*0 + 7*0 ≤ 26
0 ≤ 26
The last inequality is true, which means the first inequality is true for those x and y values. We confirm that (0,0) is a solution.
How can we tell visually based on a graph? The point (0,0) is in the shaded solution set. This is the region below the line 4x+7y = 26; this boundary line passes through (-4,6) and (3,2). Refer to the graph below.
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We do the same thing for the coordinates of the point (2,3)
4x + 7y ≤ 26
4*2 + 7*3 ≤ 26
29 ≤ 26
The last inequality is false, so it causes a chain reaction or domino effect to make the first inequality false when x = 2 and y = 3 pair up together.
(2,3) is NOT a solution
We can quickly determine this by noticing (2,3) is not in the shaded region.
Side note: Points on the boundary are part of the solution set because of the "or equal to" in the inequality sign.
Refer to the graph below. I used GeoGebra to make the graph. Desmos is another good option that I recommend.