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 :
[tex]3x+3y=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-9x-9y=-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Dividing equation (i) by 3 and equation (ii) by -9, we get
[tex]\dfrac{3x+3y}{3}=\dfrac{10}{3}\\\\\\\Rightarrow x+y=\dfrac{10}{3}[/tex]
and
[tex]\dfrac{-9x-9y}{-9}=\dfrac{-30}{-9}\\\\\\\Rightarrow x+y=\dfrac{10}{3}.[/tex]
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.
