Solve graphically the system of linear equations: 4x – 3y + 4 = 0 and 4x + 3y – 20 = 0
Find the area bounded by these lines and x-axis.
Answers
Given: System of linear equations:
4x – 3y + 4 = 0 ………..(1)
4x + 3y – 20 = 0 ………(2)
Solution :
For eq 1 :
When x = 2 ,then y = 4
When x = - 1 , then y = 0
4x – 3y + 4 = 0 passes through (2, 4) and (-1, 0,)
For eq 2 :
When x = 5 ,then y = 0
When x = 2 , then y = 4
4x + 3y – 20 = 0 passes through (5, 0) , (2, 4)
Two lines intersect at a point A (2,4) .
Hence x is 2 and y is 4.
These two lines meet x axis at B (- 1,0) and C(5,0)
Area of shaded region = Area of ABC
Area of shaded region= ½ base × height
Area of shaded region = ½ BC × AD
Area of shaded region = ½ 6 × 4
[from graph BC = 6 and AD = 4 ]
Area of shaded region = 12 sq units .
Hence , Area of the shaded region is 12 sq units.
Table and the Graph of the given systems of equations are in the attachment below :
Method to draw a graph :
To draw the graph of a linear equation in two variable a series of steps to be followed which is given below:
Step I:Obtain the linear equation. Let the equation be ax + by + c = 0
Step II: Express one unknown quantity in terms of other here. Express y in terms of x to get y = - (ax + c /b)
Step III: For any two values of x, calculate the corresponding values of y from the expression in step II to obtain two solutions say (x1, y1 and( x2 ,y2)
Step IV: plot the points (x1, y1 and( x2 ,y2) on graph paper on a suitable scale.
Step V:Draw a line passing through points marked in step IV. The line so obtained is the graph of the equation ax + by + c = 0
HOPE THIS ANSWER WILL HELP YOU……
Some more questions :
Solve the following systems of equations graphically:
x-2y=6
3x-6y=0
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Solve the following systems of equations graphically:
x+y=4
2x-3y=3
https://brainly.in/question/15918174
Step-by-step explanation:
When x = 2 , then y = 4
4x + 3y – 20 = 0 passes through (5, 0) , (2, 4)
Two lines intersect at a point A (2,4) .
Hence x is 2 and y is 4.