Answer:
The system will have infinite many solution.
Step-by-step explanation:
Given system of equations: 3x − 2y = 6 and 6x − 4y = 12
We have to solve for the system of equation.
Consider the given system of equations:
3x − 2y = 6 ...............(1)
6x − 4y = 12 ..............(2)
Consider equation (2) ,
6x − 4y = 12
Divide equation by 2, we get,
3x - 2y = 6
Which is same as equation (1) ,
Thus, the system will have infinite many solution.
For a system of equation having infinite solution following condition holds:
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}= \frac{c_1}{c_2}[/tex]
here, [tex]a_1=3 , b_1=-2,c_1=6\\\\a_2=6 , b_2=-4,c_2=12[/tex]
Thus, we get,
[tex]\frac{3}{6}=\frac{-2}{-4}= \frac{6}{12}=\frac{1}{2}[/tex]
Thus, the system will have infinite many solution.
