Draw the graphs of the equations 5x-y=5 and 3x-y=3.
Determine the co-ordinates of the vertices of the triangle formed by these lines and y-axis.Calculate the area of the triangle so formed.
Answers
Concept :
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 .
Solution :
Given systems of equations :
5x − y = 5……….(1)
3x − y = 3……….(2)
To find : The co-ordinates of the vertices of the triangle formed by these lines and y-axis and Calculate the area of the triangle so formed.
5x − y = 5, passes through (1, 0) and (0,-5)
3x − y = 3 passes through (1,0) and (0,- 3)
Area of ΔABD = ½ base height
Area of ΔABD = ½ (DB) (OA)
Area of ΔABD = ½ (2) (1)
Area of ΔABD = 1 sq unit
Hence, the required ΔABD whose vertices are A(1,0), B(0,5), C(0,-3) and Area of ΔABD is 1 sq unit.
Table and the Graph of the given systems of equations are in the attachment below :
Hope this answer will help you…
Some more questions from this chapter :
Draw the graphs of the equations x − y + 1 = 0 and 3x + 2y − 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
https://brainly.in/question/1345024
Solve the following systems of equations graphically:
x + y = 3
2x + 5y = 12
https://brainly.in/question/15918168
Step-by-step explanation:
See the attachment !!!!
