Answer:
The given system of equation have one solution.
Step-by-step explanation:
The given system of equations is
[tex]2x+3y=1[/tex]
[tex]-3x-2y=-1[/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 equation,
[tex]a_1=2,b_1=3,c_1=1,a_2=-3,b_2=-2, c_2=-1[/tex]
[tex]\frac{a_1}{a_2}=\frac{2}{-3}=-\frac{2}{3}[/tex]
[tex]\frac{b_1}{b_2}=\frac{3}{-2}=-\frac{3}{2}[/tex]
Since [tex]\frac{a_1}{a_2}neq \frac{b_1}{b_2}[/tex], therefore the given system of equation have one solution.
