3.
Which of the graphs best suits the inequality
$x$ - $y$ > - 1?
Solution:
x -
y > - 1
[Original inequality.]
x -
y = - 1
[Write corresponding equation].
y =
x + 1
[Subtract
x from each side].
The corresponding equation in slope-intercept form is
y =
x + 1.
The graph of the line has a slope of 1 and a
y-intercept of 1. Since the inequality is > use a dashed line.
The point (0, 0) satisfies the inequality. So, the solution is the half of the plane that includes the point (0, 0).
Therefore, graph 1 best suits the inequality
x -
y > - 1.
Correct answer : (1)
4.
Which of the following ordered pairs is not a solution of the inequality 3$x$ - 4$y$ > -4?
Solution:
3x - 4y > -4
[Write original inequality.]
3(4) - 4(3) > -4
[Replace x with 4 and y with 3.]
0 > -4, which is true.
[Simplify.]
So, the ordered pair (4, 3) is a solution.
3x - 4y > -4
[Write original inequality.]
3(7) - 4(3) > -4
[Replace x with 7 and y with 3.]
9 > -4, which is true.
[Simplify.]
So, the ordered pair (7, 3) is a solution.
3x - 4y > -4
[Write original inequality.]
3(3) - 4(- 4) > -4
[Replace x with 3 and y with - 4.]
25 > -4, which is true.
[Simplify.]
So, the ordered pair (3, - 4) is a solution.
3x - 4y > -4
[Write original inequality.]
3(- 3) - 4(3) > -4
[Replace x with - 3 and y with 3.]
- 21 > -4, which is not true.
[Simplify.]
So, the ordered pair (- 3, 3) is not a solution.
Therefore, (- 3, 3) is not a solution for the inequality 3x - 4y > -4.
Correct answer : (4)
5.
Choose the ordered pair that is not the solution of the inequality whose graph is shown.
Solution:
The y-intercept of the line is - 4 and the slope is 1.
The equation of the line in slope-intercept form is y = x - 4.
[Substitute m = 1 and b = - 4 in the equation y = mx + b.]
As the boundary line is a dashed line and the region below the line is shaded, the inequality should be y < x - 4.
y < x - 4
[Write original inequality.]
- 4 < 2 - 4
[Replace x with 2 and y with - 4.]
- 4 < - 2, which is true.
[Simplify.]
So, the ordered pair (2, - 4) is a solution.
y < x - 4
[Write original inequality.]
- 2 < 4 - 4
[Replace x with 4 and y with - 2.]
- 2 < 0, which is true.
[Simplify.]
So, the ordered pair (4, - 2) is a solution.
y < x - 4
[Write original inequality.]
- 4 < 4 - 4
[Replace x with 4 and y with - 4.]
- 4 < 0, which is true.
[Simplify.]
So, the ordered pair (4, - 4) is a solution.
y < x - 4
[Write original inequality.]
2 < - 2 - 4
[Replace x with - 2 and y with 2.]
2 < - 6, which is not true.
[Simplify.]
So, the ordered pair (- 2, 2) is not a solution.
Therefore, (- 2, 2) is not a solution for the inequality of the graph shown.
Correct answer : (4)
6.
Which of the following ordered pairs is not a solution of the inequality $x$ - $\frac{y}{5}$ > 6?
Solution:
x - y5 > 6
[Original inequality.]
3 - 55 > 6
[Replace x with 3 and y with 5.]
2 > 6, which is not true.
[Simplify.]
So, the ordered pair (3, 5) is not a solution.
x - y5 > 6
[Original inequality.]
8 - (- 55) > 6
[Replace x with 8 and y with - 5.]
9 > 6, which is true.
[Simplify.]
So, the ordered pair (8, - 5) is a solution.
x - y5 > 6
[Original inequality.]
11 - (05) > 6
[Replace x with 11 and y with 0.]
11 > 6, which is true.
[Simplify.]
So, the ordered pair (11, 0) is a solution.
x - y5 > 6
[Original inequality.]
0 - (- 405) > 6
[Replace x with 0 and y with - 40.]
8 > 6, which is true.
[Simplify.]
So, the ordered pair (0, - 40) is a solution.
The ordered pair (3, 5) is not a solution of the inequality x - y5 > 6.
Correct answer : (2)
7.
Which of the following is a linear inequality with two variables?
Solution:
A linear inequality in two variables will contain only two variables and an inequality symbol like ≠, ≤, <, ≥ or >.
Among the choices, 6x + 2y ≥ 6 is a linear inequality in two variables x and y.
Correct answer : (4)
8.
Identify the inequality which has the ordered pair (2, - 3) as a solution.
Solution:
5x + 3y ≤ 0
5(2) + 3(- 3) ≤ 0
[Replace x with 2 and y with - 3.]
1 ≤ 0, which is false.
[Simplify.]
5x - 3y < 0
5(2) - 3(- 3) < 0
[Replace x with 2 and y with - 3.]
19 < 0, which is false.
[Simplify.]
5x - 3y ≤ 0
5(2) - 3(- 3) ≤ 0
[Replace x with 2 and y with - 3.]
19 ≤ 0, which is false.
[Simplify.]
5x + 3y ≥ 0
5(2) + 3(- 3) ≥ 0
[Replace x with 2 and y with - 3.]
1 ≥ 0, which is true.
[Simplify.]
So, (2, - 3) is a solution of 5x + 3y ≥ 0.
Correct answer : (4)
9.
Choose the inequality which has the ordered pair (0, 0) as the solution.
Solution:
3x + 3y > 4
3(0) + 3(0) > 4
[Replace x with 0 and y with 0.]
0 > 4, which is false.
[Simplify.]
3x - 3y > 4
3(0) - 3(0) > 4
[Replace x with 0 and y with 0.]
0 > 4, which is false.
[Simplify.]
- 3x + 3y > 4
- 3(0) + 3(0) > 4
[Replace x with 0 and y with 0.]
0 > 4, which is false.
[Simplify.]
3x - 3y < 4
3(0) - 3(0) < 4
[Replace x with 0 and y with 0.]
0 < 4, which is true.
[Simplify.]
So, (0, 0) is a solution of the inequality 3x - 3y < 4.
Correct answer : (4)
10.
Choose the inequality which has the ordered pair (0, - $\frac{4}{3}$ ) as a solution.
Solution:
2x - 3y > 0
2(0) - 3(- 43 ) > 0
[Replace x with 0 and y with - 4 / 3.]
4 > 0, which is true.
[Subtract.]
2x - 3y < 0
2(0) - 3(- 43 ) < 0
[Replace x with 0 and y with - 4 / 3.]
4 < 0, which is false.
[Subtract.]
2x + 3y > 0
2(0) + 3(- 43 ) > 0
[Replace x with 0 and y with - 4 / 3.]
- 4 > 0, which is false.
[Subtract.]
3x + 2y ≥ 0
3(0) + 2(- 43 ) ≥ 0
[Replace x with 0 and y with - 4 / 3.]
- 83 ≥ 0, which is false.
[Subtract.]
So, the ordered pair (0, - 4 / 3 ) is a solution to the inequality 2x - 3y > 0.
Correct answer : (4)