Solving Systems of Linear Inequalities Answers
Which ordered pairs make both inequalities true? Check all that apply.
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(–4, –2)✔ (–1, –2)X (1, 4)(2, 2)
Graphically, a point is a solution to a system of two inequalities if and only if the point
Which linear inequality will not have a shared solution set with the graphed linear inequality?
Which system of inequalities with a solution point is represented by the graph?
Which equation represents an inequality in the system of inequalities shown in the graph?
y > 2x +2y > –2x – 1y < 2x + 2y < –2x – 1
Which statements are true about the graph of y ≤ 3x + 1 and y ≥ –x + 2? Check all that apply.The slope of one boundary line is 2.Both boundary lines are solid.A solution to the system is (1, 3).Both inequalities are shaded below the boundary lines.The boundary lines intersect.
Mr. Hernandez plotted the point (1, 1) on Han’s graph of y ≤ One-half x + 2. He instructed Han to add a second inequality to the graph that would include the solution (1, 1).Which equation could Miguel write?
Which ordered pairs make both inequalities true? Check all that apply.
Graphically, a point is a solution to a system of two inequalities if and only if the point
Which linear inequality will not have a shared solution set with the graphed linear inequality?
Which is the graph of the system x + 3y > –3 and y < x + 1?
Which system of inequalities with a solution point is represented by the graph?
Which statements are true about the graph of y ≤ 3x + 1 and y ≥ –x + 2? Check all that apply.The slope of one boundary line is 2.Both boundary lines are solid.A solution to the system is (1, 3).Both inequalities are shaded below the boundary lines.The boundary lines intersect.
How will the solution of the system y > 2x + and y 2x + ?
The system of linear inequalities has no solution. Both equations have the same slope of -1, which means the boundary lines are parallel. Since the first inequality describes the region above the line $y = -x + 3$ and the second inequality describes the region below the line $y = -x - 2$, the shaded regions move in opposite directions and do not overlap. Because there are no points in common, the system has no solution.
Mr. Hernandez plotted the point (1, 1) on Han’s graph of y ≤ One-half x + 2. He instructed Han to add a second inequality to the graph that would include the solution (1, 1).Which equation could Miguel write?
Determine the relationship between the point (1, –5) and the given system of inequalities.y ≤ 3x + 2y > –2x – 3Explain your answer both algebraically and graphically.
Algebraically, substituting (1, -5) into the inequalities yields -5 ≤ 3(1) + 2, which simplifies to -5 ≤ 5 (true), and -5 > -2(1) - 3, which simplifies to -5 > -5 (false). Graphically, the point (1, -5) lies within the shaded region of the first inequality's solid line but lies directly on the dashed boundary line of the second inequality. Because points on a dashed line are excluding, and the second inequality is not satisfied, (1, -5) is not a solution to the system.
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