show graphically that the pair of equations 8x+5y=9,16x+10y=27 has no solution Related: Assignment - Linear Equation in two Variables, Class 10 Mathematics?

Question

show graphically that the pair of equations 8x+5y=9,16x+10y=27 has no solution Related:  Assignment - Linear Equation in two Variables, Class 10 Mathematics?

Answer

Answer

Answer

Introduction:
Linear Equations in two variables are equations that involve two variables, generally x and y, and can be represented graphically as straight lines on a coordinate plane. In this problem, we are given two equations and we have to show that they have no solution.

Method:
To show that the given pair of equations has no solution, we need to graphically represent them and see if they intersect or not. If the lines intersect, then there is a solution, but if they are parallel, then there is no solution.

Graphical Representation:
Let's first write the given equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Equation 1: 8x - 9/5 = y/5 or y = 8x - 9/5
Equation 2: 16x - 27/10 = y/10 or y = 16x - 27/10
Now, let's plot these two lines on a coordinate plane. We can do this by finding two points on each line and connecting them with a straight line.
For Equation 1, let x = 0, then y = -9/5. This gives us the point (0,-9/5).
Let x = 1, then y = 3/5. This gives us the point (1,3/5).
Connecting these two points, we get the line L1.
For Equation 2, let x = 0, then y = -27/10. This gives us the point (0,-27/10).
Let x = 1, then y = -11/10. This gives us the point (1,-11/10).
Connecting these two points, we get the line L2.
Now, let's plot these two lines on the same coordinate plane.

Conclusion:
From the graph, we can see that the two lines are parallel and do not intersect at any point. Therefore, there is no solution to the given pair of equations.

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