-In the system of equations in x and y, 2x+3y=12, 4x+ay=16, where a is an integer, what would a have to be for the equations to be inconsistent? -In the system of equations in x and y, 2x+3y=12, 4x+ay=b, where a is the answer to question 2, what would b be if the equations are dependent?

Step 1
To find value of a such that the system of equations 2x+3y=124x+ay=16 is inconsistent.
Using this value of a, to find value of b such that the system of equations 2x+3y=124x+ay=b is dependent.
Step 2
Let the system of equations be
${\displaystyle a_{1}x+b_{1}y+c_1=0}$
${\displaystyle a_{2}x+b_{2}y+c_2=0}$
${\displaystyle \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}}$
Thus, for given system of equations
${\displaystyle \frac{2}{4}=\frac{3}{a}\ne -\frac{12}{-16}}$
${\displaystyle \frac{1}{2}=\frac{3}{a}}$
a=6
Step 3
System of equations is dependent, if
${\displaystyle \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}}$
Thus, for given system of equations
${\displaystyle \frac{2}{4}=\frac{3}{a}=-\frac{12}{-b}}$
${\displaystyle =\frac{3}{6}=\frac{12}{b}}$
${\displaystyle \frac{1}{2}=\frac{12}{b}}$
b=24