Substitute the given point in both inequalities. Do you get a true or a false statement?
No
Practice makes perfect
We have a System of Inequalities and are asked if the given point satisfies either inequality and is a solution of the system.
y<2x+5 & (I) 4y>-4x-8 & (II)
To check if the point (-1,-2) satisfies either inequality, we can substitute (-1,-2) into the inequalities. If after substituting and simplifying we get a true statement, then we say that the point satisfies the inequality. If it satisfies both inequalities, then it is a solution to the system.
y<2x+5 & (I) 4y>-4x-8 & (II)
(I), (II):x= -1, y= -2
-2? <2( -1)+5 4( -2)? >-4( -1)-8
(I), (II):Multiply
-2? <-2+5 -8? >4-8
(I), (II):Add and subtract terms
-2<3 -8≯-4
We obtained a true statement from only one inequality. This means that the point (-1,-2) does not satisfy both inequalities, so it is not a solution to the system.
