Page 10 - 1202 Question Bank Mathematics Form 4

Chapter 6 Linear Inequalities in
Two Variables

NOTes

6.1 Linear Inequalities in Two Variables
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1. Linear inequalities in two variables is the inequality that involved two variables such that the highest power of both
variables is 1. Table below shows the inequality that is suitable for certain situations.

Situation Linear Inequality Situation Linear Inequality
y is more than x y . x y is at most h times of x y < hx
y is less than x y , x The maximum value of y is h. y < h
The minimum value of y is h. y > h
y is not more than x y < x
The sum of x and y is at least k. x + y > k
y is not less than x y > x
3
3
y is at least h times of x. y > hx The ratio of x to y is not less than . y < x
2
2

2. Dotted line ( ) is used for the inequalities that 4. All the points located on the straight line y = mx + c
has the sign . or , and solid line ( ) is used for satisfied the equation y = mx + c.
the inequalities that has the sign > or <. 5. All the points in the region above the straight line
3. Linear inequalitis for the straight line on the graph y = mx + c satisfy the inequality y . mx + c.
can be determined using the general form equation 6. All the points in the region below the straight line
of the straight line, y = mx + c such that m is the y = mx + c satisfy the inequality y , mx + c.
gradient of the straight line and c is the y-intercept.
7. Diagram below shows a few regions that satisfy the
certain inequalities.
Linear Inequality
y > mx + c, the region is y , mx + c, the region is y < h, the region is x , k, the region is on the
above the solid line below the dashed line below the solid line y = h left side of the dashed line
y = mx + c y = mx + c x = k

y y = mx + c y y y x = k
y > h
y < mx + c y = h x < k x > k
y > mx + c y > mx + c
y < mx + c
x x x x
0 0 0 0
y < h
y = mx + c

6.2 Systems of Linear Inequalities in Two Variables
1. A combination of two or more linear inequalities is known as a system of linear inequalities.

2. The region that satisfy a system of linear inequalities can be determined by using y x = 2
the following steps:
I Determine and mark the region that is represented by each linear inequalities.
II Determine the common region that satisfies all the linear inequalities.
III Shade the region and make sure the region is being bounded by all the linear
R
inequalities.
2
3. For example, the shaded R in the diagram on the left satisfies all the inequalities 2 0 2 x
of y < 3x + 2, y > –x + 2 and x , 2. – – 3 y = –x + 2
y = 3x + 2

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C06 1202QB Maths Form 4.indd 50 21/02/2022 10:45 AM