QQuestionMathematics
QuestionMathematics
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.
y, is greater than, minus, one half, x, minus, 3
y>−
2
1
x−3
y, is greater than, x, plus, 6
y>x+ 6
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Answer
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Step 1: Graph the first inequality, y > - 1 / 2 * x - 3.
First, rewrite the inequality in slope-intercept form (y = mx + b) to find the slope and y-intercept. y > - 1 / 2 * x - 3.5 The slope is - 1 / 2 and the y-intercept is 3.5. Plot the line with a dashed style since the inequality is strict (y is greater than, not greater than or equal to). To indicate the solution set, shade above the line.
Step 2: Graph the second inequality, y > x + 6.
Rewrite the inequality in slope-intercept form. y > x + 6 The slope is 1 and the y-intercept is 6. Plot the line with a dashed style and shade above the line to indicate the solution set.
Final Answer
The solution set of the system of inequalities is the area above both lines. A point in the solution set is (13 / 3, - 11 / 6).
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