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 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

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Example

Graph the system of inequalities.
 xx - 2y ≤ 0 > 2

Solution

Step 1 Solve the first inequality for y. Then graph the inequality.

The first inequality does not contain the variable y.

To graph the first inequality, x 0, first graph the corresponding equation, x = 0.

 This is a vertical line that passes through the x-axis at the point (0, 0); it is the y-axis.

For the inequality x 0, the inequality symbol is . This stands for is less than or equal to.

 To represent equal to, draw a solid line along the y-axis.

 To represent less than, shade the region to the left of the line. Each point in that region has an x-coordinate less than 0. Step 2 Solve the second inequality for y. Then graph the inequality.

To solve x - 2y > 2 for y, do the following:

 Subtract x from both sides. - 2y > - x + 2 Divide both sides by -2. Be sure to reverse the inequality symbol because you are dividing by a negative number. Simplify. To graph , first graph the equation .

 The y-intercept is (0, -1). Plot (0, -1).

 The slope is . To find a second point on the line, start at (0, -1) and move up 1 and right 2 to the point (2, 0). Plot (2, 0).

 Since the inequality symbol < does not contain equal to, draw a dotted line through (0, -1) and (2, 0).

 To represent less than, shade the region below the line. Step 3 Shade the region where the two graphs overlap.

The solution is the region where the graphs overlap. The solution of the system is the dark shaded region.

As a check, choose a point in the solution region.

For example, choose ( -1, -5).

To confirm that ( -1, -5) is a solution of the system, substitute -1 for x and -5 for y in each of the original inequalities and simplify.

 First inequality Second inequality x Is -1 ≤ 0 ≤ 0 ? Yes Is Is Is x - 2y -1 - 2(-5) -1 + 10 9 > 2> 2 ? > 2 ? > 2 ? Yes

Since ( 1, 5) satisfies each inequality, it is a solution of the system. 