Solve each of the following systems of simultaneous inequations:
3x + 4y ≥ 12, x ≥ 0, y ≥ 1 and 4x + 7y≤28
Consider the inequation 3x + 4y ≥ 12 :
⇒4y ≥ 12 - 3x
⇒y ≥ 3 -
Consider the equation y = 3 -
Finding points on the coordinate axes:
If x = 0, the y value is 3 i.e, y = 3
⇒ the point on the Y axis is A(0,3)
If y = 0, 0 = 3 -
⇒x = 4
The point on the X axis is B(4,0)
Now consider the inequality y ≥ 3 -
Here we need the y value greater than or equal to y ≥ 3 -
⇒ the required region is above point A.
Therefore the graph of the inequation y ≥ 3 - is fig. 9a
Fig 9a
Consider the inequation 4x + 7y≤28
⇒ 7y≤28 - 4x
⇒y≤4 -
Consider the equation y = 4 -
Finding points on the coordinate axes:
If x = 0, the y value is 4 i.e, y = 4
⇒ the point on the Y axis is C(0,4)
If y = 0, 0 = 4 -
⇒x = 7
The point on the X axis is D(7,0)
Now consider the inequality y≤4 -
Here we need the y value less than or equal to 4 -
⇒ the required region is below point C.
Therefore the graph of the inequation y≤4 - is fig. 9b
Fig 9b
x ≥ 0 is the region right side of Y - axis.
y ≥ 1 is the region above the line y = 1
Combining all the above results in a single graph , we’ll get
The solution of the system of simultaneous inequations is the intersection region of the solutions of the two given inequations.