Solve the following system of inequalities graphically:
$$
2 x+y \geq 4, x+y \leq 3,2 x-3 y \leq 6
$$

Answer

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Algebra

NCERT Class 11 - Math

Chapter 6

Linear Inequalities

Section 3

Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation

Discussion

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Video Transcript

were given that any qualities three. X plus two where is greater than or equal to six and for X minus Y is greater than or equal to two and asked to find a solution to the to any qualities easing graphing. So the first inequality graft is three X plus two y is greater than or equal to six. It has a Y intercept of +03 and a slip of negative 3/2 since it goes down three and over to to the right. This is consistent with the equation, and anything to the right of the line is shooted block. Our next inequality craft is for X minus Y is greater than or equal to two. It has a Y intercept of zero negative two, which is consistent with the equation and is slope of four, since it goes up for and over one, which is also consistent with the equation. The region where both of these inequalities overlap is the solution, and this can be seen to be the region over here on the right side, since both the black and the red initiating a to come up with an equation that only symbolizes the solution For both of these equations, we can add a limit to the first equation or inequality. Sorry, with the second inequality as it's bound. And then take this off. And we're left with this black shaded region being our solution, since it shows the region where both of the inequalities intersected or overlapped in the graph. So this is our answer.

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