Answer:
Independent
Step-by-step explanation:
We need to find whether the system of equations [tex]-2-y=9[/tex] and [tex]3x-4y=-8[/tex] are independent, dependent, or inconsistent.
Now, we know that the general form of a linear equation in two variables is [tex]ax+by+c=0[/tex]
So, the general form of the given equations is [tex]-y-11=0[/tex] and [tex]3x-4y+8=0[/tex]
Now, for a system of equations [tex]a_{1}x+b_{1}y+c_{1}=0[/tex] and [tex]a_{2}x+b_{2}y+c_{2}=0[/tex] , we need to find [tex]\frac{a_{1}}{a_{2}}[/tex], [tex]\frac{b_{1}}{b_{2}}[/tex], and [tex]\frac{c_{1}}{c_{2}}[/tex]
Now, [tex]\frac{a_{1}}{a_{2}}=\frac{0}{3}[/tex]
[tex]\frac{b_{1}}{b_{2}}=\frac{-1}{-4}=\frac{1}{4}[/tex]
So, we have [tex]\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}[/tex]
Hence, the system of equations are independent.
