Question

By comparing the ratios of the coefficients, find whether the pair of equations x + 2y + 5 = 0 and

-3x - 6y + 1 = 0 are consistent or inconsistent.​

Answer 1

Step-by-step explanation:

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

Thanks.

Answer 2

Answer:

Step-by-step explanation:

x+2y+5=0

-3x-6y+1=0

$a_{1} =1,b_{1} =2,c_{1} =5$

$a_{2} = -3,b_{2} =-6,c_{2} =1$

$\frac{a_{1} }{a_{2} } =\frac{1}{-3},\frac{b_{1} }{b_{2} } =\frac{2}{-6} =\frac{1}{-3} .\frac{c_{1} }{c_{2} } =\frac{5}{1}$

$\frac{a_{1} }{a_{2} }=\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }$

since the equation forms a parallel line

therefore it is inconsistent