The required solution to the system of inequalities [tex]2x+3y > 12, x -y\geq 1[/tex] is (5, 2). Option D is correct.
Given,
Systems of inequalities are given solution to inequalities to be determined.
[tex]\left \{ {{2x+3y > 12} \atop {x -y\geq 1}} \right.[/tex]
What is inequality?
Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
[tex]\left \{ {{2x+3y > 12} \atop {x -y\geq 1}} \right.[/tex]
Here,
2x +3y = 12 - - - - - (1)
x - y = 1 - - - - - -(2)
From equation 2
x = y + 1
Put x into equation 1
2( y + 1 ) + 3y = 12
2y + 2 + 3y = 12
5y = 12 -2
y =10/5
y = 2
Now put y = 2 in equation (1)
2x + 3(2) = 12
2x + 6 = 12
x = 3
It is to be verified that value of x should be greater or equal to 3 and y should be greater or equal to 2 in order to have the solution to a system of inequalities. i.e. x ≥3 and y ≥ 2. from observation of the option it is seen that option D (5, 2) has the required solution.
Thus, the required solution to the system of inequalities [tex]2x+3y > 12, x -y\geq 1[/tex] is (5, 2). Option D is correct.
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