The solution to the system of inequalities is (2.2,-1.9)
Explanation:
Given that the system of inequalities are [tex]12 x+6 y \geq 15[/tex] and [tex]4 x-8 y>24[/tex]
We need to determine the solution of the equation.
Let us plot the inequality [tex]12 x+6 y \geq 15[/tex] in the graph.
Substituting the coordinate (0,0) in the inequality [tex]12 x+6 y \geq 15[/tex], we have,
[tex]12(0)+6(0)\geq 15[/tex]
[tex]0\geq 15[/tex]
Since, the coordinate (0,0) does not satisfy the inequality [tex]12 x+6 y \geq 15[/tex], then the line of the inequality does not pass through the coordinate (0,0)
Thus, let us shade the upper part of the inequality.
Now, we shall plot the inequality [tex]4 x-8 y>24[/tex] in the graph.
Substituting the coordinate (0,0) in the equality [tex]4 x-8 y>24[/tex], we have,
[tex]4(0)-8(0)>24[/tex]
[tex]0>24[/tex]
Since, the coordinate (0,0) does not satisfy the inequality [tex]4 x-8 y>24[/tex], then the line of the inequality does not pass through the coordinate (0,0)
Thus, let us shade the lower part of the inequality.
The solution to the system of inequalities is the point of intersection of these lines.
Thus, the lines intersect at the point (2.2, -1.9)
Thus, the solution is (2.2, -1.9)
