Question

Equations must be solved simultaneously of those lines intersecting at points to determine

Answer 1

Answer:

To solve a system graphically, find the point of interesection of the lines.

Because it is not always easy to determine where the graphs intersect, this method may not always be used, so, another system must be used to find the point of interesection of the lines, the solution.

If each line in the system has the same slope and the same y-intercept, the lines are coincident.

For example:

equations-

x–2y = 1

2x–4y = 2

Solution: To check the condition of consistency we need to find out the ratios of the coefficients of the given equations,

a1/a2 = 1/2

b1/b2 = 1/2

c1/c2 = 1_2

Now, as a1/a2 = b1/b2 = c1_c2 we can say that the above equations represent lines which are coincident in nature and the pair of equations is dependent and consistent.

There is no point of intersection between these two lines. Every point on the line represented by x - 2y = 1 is present on the line represented by 2x -4y = 2. Hence, this pair of equations has an infinite number of solutions.

Also, when we plot the given equations on graph, it represents a pair of coincident lines

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