6. Systems of Linear Inequalities
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x=2, y=12
(I), (II): Multiply
(I), (II): Add terms
We could also verify that the point satisfies the system by graphing the system. When graphing a system of inequalities, we begin by drawing the boundary lines of the regions. In our case, the boundary lines are going to be dashed lines because both inequalities are strict.
In Equation (I), the y-values must all be greater than 2x+4, so we need to shade above this line. In Equation (II), the y-values must all be less than 3x+7, so we will to shade below this line.
Finally, we plot the given point and check whether or not it falls within the overlapping region.
It does! Therefore, we know that the point satisfies the given system.