You only need to find these symbols <, > , ≤, ≥ for the equation to become a linear inequality
2.) C
because the value is false
if (2, 6)
x - y ≤ - 3
2 - 6 ≤ -3
-4 ≤ -3 ; true
x + y ≥ -1
2 + 6 ≥ - 1
8 ≥ -1 ; true
if (-1, 3)
x - y ≤ - 3
-1 - 3 ≤ -3
-4 ≤ -3 ; true
x + y ≥ -1
-1 + 3 ≥ -1
2 ≥ -1 ; true
if (1, -1)
x - y ≤ - 3
1 - (-1) ≤ -3
2 ≤ - 3 ; false
x + y ≥ -1
1 + (-1) ≥ -1
0 ≥ -1 ; false
if (-1, 3)
x - y ≤ - 3
-1 - 3 ≤ -3
-4 ≤ - 3 ; true
x + y ≥ -1
-1 + 3 ≥ - 1
2 ≥ -1 ; true
3.) C. Graphical
graphing because the range of solutions can be easily expressed.
4.) Karen works as an online tutor (x) for php150 per hour. She also works as editor (y) for Php250 per hour. She is only allowed to work 17 hours per week. She wants to make at most Php 3000. Write a system of linear inequalities in two variables and give 2 solutions.
Solution:
Let x be hours as an online tutor
Ley y be hours as an editor
Equation 1:
x + y ≤ 17
Equation 2:
150x + 250y ≤ 3000
(2, 1)
x + y ≤ 17
2 + 1 ≤ 17
3 ≤ 17 ; true
150x + 250y ≤ 3000
150(2) + 250(1) ≤ 3000
300 + 250 ≤ 3000
550 ≤ 3000 ; true
(10, 5)
x + y ≤ 17
10 + 5 ≤ 17
15 ≤ 17 ; true
150x + 250y ≤ 3000
150(10) + 250(5) ≤ 3000
1500 + 1250 ≤ 3000
2750 ≤ 3000 ; true
system of linear inequalities in two variables
x + y ≤ 17
150x + 250y ≤ 3000
2 solutions. to inequalities
(2, 1)
(10, 5)
5.) C
2x + y ≥ 7
x + y ≤ 19
keyword is atleast 7 points and at most 19 points
6.) B
7.) A
(2, 2)
2x + y ≥ 7
2(2) + 2 ≥ 7
4 + 2 ≥ 7
6 ≥ 7 ; false
(2, 2)
x + y ≤ 19
2 + 2 ≤ 19
4 ≤ 19 ; true
SHOULD be BOTH true in order for the value to be an ordered pair
Answers & Comments
1.) D
x + 3 y≥ 5
y - 5x ≤ -8
You only need to find these symbols <, > , ≤, ≥ for the equation to become a linear inequality
2.) C
because the value is false
if (2, 6)
x - y ≤ - 3
2 - 6 ≤ -3
-4 ≤ -3 ; true
x + y ≥ -1
2 + 6 ≥ - 1
8 ≥ -1 ; true
if (-1, 3)
x - y ≤ - 3
-1 - 3 ≤ -3
-4 ≤ -3 ; true
x + y ≥ -1
-1 + 3 ≥ -1
2 ≥ -1 ; true
if (1, -1)
x - y ≤ - 3
1 - (-1) ≤ -3
2 ≤ - 3 ; false
x + y ≥ -1
1 + (-1) ≥ -1
0 ≥ -1 ; false
if (-1, 3)
x - y ≤ - 3
-1 - 3 ≤ -3
-4 ≤ - 3 ; true
x + y ≥ -1
-1 + 3 ≥ - 1
2 ≥ -1 ; true
3.) C. Graphical
graphing because the range of solutions can be easily expressed.
4.) Karen works as an online tutor (x) for php150 per hour. She also works as editor (y) for Php250 per hour. She is only allowed to work 17 hours per week. She wants to make at most Php 3000. Write a system of linear inequalities in two variables and give 2 solutions.
Solution:
Let x be hours as an online tutor
Ley y be hours as an editor
Equation 1:
x + y ≤ 17
Equation 2:
150x + 250y ≤ 3000
(2, 1)
x + y ≤ 17
2 + 1 ≤ 17
3 ≤ 17 ; true
150x + 250y ≤ 3000
150(2) + 250(1) ≤ 3000
300 + 250 ≤ 3000
550 ≤ 3000 ; true
(10, 5)
x + y ≤ 17
10 + 5 ≤ 17
15 ≤ 17 ; true
150x + 250y ≤ 3000
150(10) + 250(5) ≤ 3000
1500 + 1250 ≤ 3000
2750 ≤ 3000 ; true
system of linear inequalities in two variables
x + y ≤ 17
150x + 250y ≤ 3000
2 solutions. to inequalities
(2, 1)
(10, 5)
5.) C
2x + y ≥ 7
x + y ≤ 19
keyword is atleast 7 points and at most 19 points
6.) B
7.) A
(2, 2)
2x + y ≥ 7
2(2) + 2 ≥ 7
4 + 2 ≥ 7
6 ≥ 7 ; false
(2, 2)
x + y ≤ 19
2 + 2 ≤ 19
4 ≤ 19 ; true
SHOULD be BOTH true in order for the value to be an ordered pair
8.) B
Di po maaninag ang graph.
9.) B
10.) A, B, C, F
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