Solving systems of linear equations

Determine the relationship betwen the point (1,-5) and the given system of inequalities. Y is less than it equal to 3x + 2, y > -2x - 3. Explain your answer both algebraically and graphically.

Algebraically, the point (1,-5) satisfies the first inequality, but it does not satisfy the second inequality be ause -5 is not greater than -5. Graphically, the point (1,-5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore (1,-5) is not a solution to the given system of inequality.

Which statements are true about the graph of y is less than or equal to 3x + 1 and y is greater than or equal to -x + 2? Check all that apply.

The slope of one boundary line is 2. (NO) Both boundary lines are solid. (YES) A solution to the system is (1,3). (YES) Both inequalities are shaded below the boundary lines. (NO) The boundary lines intersect. (YES)

How will the solution of the system y > 2x + 2/3 and y < 2x + 1/3 change if the inequality sign on both inequalities is reversed to y < 2x + 2/3 and y > 2x + 1/3?

There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the solution has an intersection with an infinite number of solutions.

Mr. Hernandez plotted the point (1,1) on Han's graph of y is less than or equal to 1/2x + 2. He instructed Han to add a second inequality to the graph that would include the solution (1,1). Which equation could Miguel write?

Y is less than or equal to 2x - 1.