Solve the following inequalities graphically on the set of axes below state the coordinates of a point in the solution set
1 answer:
Answer:
A solution point is (2,2)
Step-by-step explanation:
Graph the lines. If it is just greater that or less than, use dashed lines. I fits greater than or equal too, or other symbols like that, use a solid line
Use the test point (0,0). If it satisfies the inequality, shade the side of the graph with that point (you can use any test point, not just (0,0)). If it doesn't satisfy, then shade the other side
The Shaded area shared by both lines is the area of the solution
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Answer:
B. (6, 1)
Step-by-step explanation:
A graph of the solution space shows that the point (6, 1) is the only one that satisfies both inequalities.
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<em>Verification</em>
3(6) +4(1) = 18 +4 = 22 < 24
3(6) -4(1) = 18 -4 = 14 > 12
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<em>Notes on the Solution</em>
The graphing calculator used here only recognizes variables x and y. Since g is the first variable in the ordered pair (g, z) we use x to represent g in the equations that are graphed. Similarly, y is used to represent z in the graphed equations.
You graph an inequality by graphing it as though it were an equation, then choosing the appropriate half-plane (one side of the line or the other) to shade as the solution space. Where the shadings from the two inequalities overlap, both are satisfied by points in that area.
In the first inequality, x and y values that are less than those on the line will satisfy the inequality, so the shading is below the line.
In the second inequality, x values greater than those on the line will satisfy the inequality, so the shading is to the right of the line.
In both cases, the line is graphed as a dashed line. This is because the points on the line do not satisfy the < or > conditions, so are not part of the solution set. (If one or both conditions were ≤ or ≥, then the corresponding line would be solid, and the points on the line would be part of the solution.)
