Substitute the given point in both inequalities. Do you get a true or a false statement?
Yes
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<7 8>-12
We obtained a true statement from both inequalities. This means that the point (1,2) satisfies both inequalities, so it is a solution to the system.
