Question

What is the solution of the following system?

3 x + 3 y = 10
− 9 x − 9 y = − 30

Answer 1

Answer: The given system of equations will have an infinite number of solutions.

Step-by-step explanation: We are given to find the solution to the following system of equations :

`3x+3y=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-9x-9y=-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Dividing equation (i) by 3 and equation (ii) by -9, we get

`(3x+3y)/(3)=(10)/(3)\\\\\\\Rightarrow x+y=(10)/(3)`

and

`(-9x-9y)/(-9)=(-30)/(-9)\\\\\\\Rightarrow x+y=(10)/(3).`

Since both the equations are same, so we have a linear equation in two variables x and y.

Therefore, the given system of equations will have an infinite number of solutions.