Graphing Systems of Linear Inequalities Warmup 2

Is (-2,4) a solution to the system?

• Solution

• Not a solution

Answer explanation

To determine if (-2,4) is a solution, substitute x = -2 and y = 4 into the equations of the system. If both equations are satisfied, then (-2,4) is a solution. Since it satisfies both, the answer is 'Solution'.

Match the system to the graph (solution set is on the left)

• y ≤ 3x   and  y ≤ -2x + 4

• y > 3x   and  y > -2x + 4

• y < 3x   and  y > -2x + 3

• y > 3x   and  y < -2x + 4

Answer explanation

The correct choice is 'y > 3x and y < -2x + 4' because it represents a region above the line y = 3x and below the line y = -2x + 4, matching the graph's shaded area.

This system has an infinite number of solutions, TRUE or FALSE?

• TRUE

• FALSE

Answer explanation

The statement is FALSE because a system can have a finite number of solutions or no solutions at all, depending on its constraints. An infinite number of solutions typically occurs in underdetermined systems.

Solve the system of inequalities by graphing.

• 
• 
• 
• 

Consider the function y<2x+3. Which is true?

• The line would be solid with shading above.

• The line would be dashed with shading above.

• The line would be solid with shading below.

• None of these.

Answer explanation

The inequality y < 2x + 3 indicates a dashed line (not including the boundary) with shading below the line, as it represents values less than the line. Therefore, 'None of these' is the correct choice.

Rewrite this inequality in "y=" form to graph.

3x - 6y > 12

• y > ¹/₂x - 2

• y < -¹/₂x + 2

• y < ¹/₂x - 2

• y > -3x - 2

Answer explanation

To rewrite the inequality 3x - 6y > 12 in y= form, first isolate y: -6y > -3x + 12, then divide by -6 (reversing the inequality): y < (1/2)x - 2. Thus, the correct choice is y < (1/2)x - 2.

Which of the following is NOT a solution to the systems of inequalities?

• (0, 0)

• (3, -2)

• (3, -4)

• (4, -4)

Answer explanation

The point (0, 0) does not satisfy the given systems of inequalities, making it the only option that is NOT a solution. The other points (3, -2), (3, -4), and (4, -4) meet the criteria of the inequalities.