Solve the following systems of equations graphically:
x – 2y = 5
2x + 3y = 10
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 - 2y = 5……….(1)
2x + 3y = 10……….(2)
x - 2y = 5, passes through (0,5) and (1,-2)
2x + 3y =10 passes through (0,5) and (2,2)
Two lines intersect at a point A (5, 0) .
Hence x = 5 and y = 0.
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 :
Solve the following systems of equations graphically:
x + y = 3
2x + 5y = 12
https://brainly.in/question/15918168
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
Point of intersection will be (3, -1)
Step-by-step explanation:
Given linear equations are
x – 2y = 5 ---- (1)
2x + 3y = 10 ---- (2)
Adding equations (1)*3 & 2, we get: 5x = 15. So x = 15/5 = 3
Substituting x = 3 in equation 1, we get: 3 - 2y = 5
2y = -2
y = -2/2 = -1
Hence solved. x = 3 and y = -1.
If you draw a graph for the equations, you will get two straight lines. The co-ordinates of the point of intersection of the two lines will be the solution. The co-ordinates will be (3, -1).
Point of intersection will be (3, -1)