Question

7. By drawing graphs, comment on the solvability of the following system of equations.

2y = 4x - 6 ; 2x = y + 3

Standard:- 10

Content Quality Solution Required

❎ Don't Spamming ❎

Answer 1

Hey there !

Solution :

Well let us rewrite the given equations. 

2y = 4x - 6

Transposing 4x to the LHS we get,

- 4x + 2y = - 6   ---( Equation 1 )

2x = y + 3

Transposing y to the RHS we get,

2x - y = 3   ---( Equation 2 )

Let us assemble the equations first.

- 4x + 2y = - 6
+ 2x - 1y = + 3

So we know that if, 

a₁ / a₂ = b₁ / b₂ = c₁ / c₂ 

a₁ and a₂ = Coefficients of x
b₁ and b₂ = Coefficients of y
c₁ and c₂ = Constants of the equation

Then the equations would be having infinite solutions and the graph will be having Coincident lines.

So Let us check whether the above pair of equations satisfy this condition.

- 4 / 2 = - 2

+ 2 / - 1 = - 2

- 6 / 3 = - 2

Since all the values are equal, the graph will be a co-incident line graph and the Pair of equations will be having infinite solutions.

Note : Check the attachment for the graph 

Attachment 1 = Zoomed in view

Attachment 2 = Zoomed out view

The line keeps on extending on both sides signifying that the equation has infinite solutions

Hope it helped :-)