Solve the following systems of equations graphically:
x + y = 3
2x + 5y = 12
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 :
x + y = 3 …………(1)
2x + 5y = 12……….(2)
x + y = 3 passes through (3,0) and (0,3).
2x + 5y = 12 passes through (6, 0) and (1, 2)
Two lines intersect at a point A (1, 2).
Hence x = 1 and y = 2
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 5x − y = 5 and 3x − y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.
https://brainly.in/question/1345037
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
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