7. Systems of Linear Inequalities
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Graph the inequalities individually. What region do their solution sets have in common?
The line y=x-4.
(I), (II): LHS-x=RHS-x
(I), (II): Flip inequality and change signs
y=x-4, which has a slope of 1 and a y-intercept of -4. Let's graph this boundary line twice, a red line and a blue line, representing each of the inequalities. Notice if you mix red and blue you get purple.
(I), (II): x= 0, y= 0
(I), (II): Subtract term
From the graph above, we can see that the only region both solutions sets have in common is the boundary line. Thus, the intersection is the boundary line y=x-4.