Answer:
The solution is ([tex]\frac{11}{1.5}[/tex],0)
The given system of equations have only one solution
([tex]\frac{11}{1.5}[/tex],0)
Step-by-step explanation:
Given equations are [tex]1.5x+2y=11\hfill (1)[/tex]
and [tex]3x+6y=22\hfill (2)[/tex]Now to find the number of solutions to the given system:
Multiply the equation (1) into 3 we get
[tex]4.5x+6y=33\hfill (3)[/tex]
Subtracting the equations (2) and (3) we get
4.5x+6y=33
3x+6y=22
__________
1.5x=11
[tex]x=\frac{11}{1.5}[/tex]
Substitute the value of x in equation (1) we get
[tex]1.5(\frac{11}{1.5})+2y=11[/tex]
[tex]11+2y=11[/tex]
2y=0
Therefore y=0
Therefore the solution is ([tex]\frac{11}{1.5}[/tex],0)
The given system of equations have only one solution ([tex]\frac{11}{1.5}[/tex],0)