Answer:
The correct option is 1.
Step-by-step explanation:
The system of equation is
[tex]3x+y=18[/tex]
[tex]3x+y=16[/tex]
A system of equation has two equation [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex].
1. If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex], then system of equations has no solution.
2. If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex], then system of equations has infinite solution.
3. If [tex]\frac{a_1}{a_2}neq \frac{b_1}{b_2}[/tex], then system of equation has one solution.
In the given system of equations,
[tex]a_1=3,b_1=1,c_1=8, a_2=3,b_2=1, c_2=16[/tex]
[tex]\frac{a_1}{a_2}=\frac{3}{3}=1[/tex]
[tex]\frac{b_1}{b_2}=\frac{1}{1}=1[/tex]
[tex]\frac{c_1}{c_2}=\frac{18}{16}=\frac{9}{8}[/tex]
Since [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex], therefore the system of equation has no solution.
The correct option is 1.
