### Linear Equations

goals
For the following system of equation determine the value of k for which the given system of equation has a unique solution.
$2x-3y=1$
$kx+5y=7$
$3(5m-7)-2(9m-11)=4(8m-13)-17$
Let $Ax+By=C$ and $A'x+B'y=C'$ represent two lines.
(a)  If $\displaystyle \frac{A}{A'} = \frac{B}{B'} \neq \frac{C}{C'}$, then the lines are parallel.
Above properties provide us a way to write the equation of a line parallel or perpendicular to a given line that contains a given point not on the line. For example, suppose that we want the equation of the line pependicular to $3x+4y=6$ that contains the point (1, 2). The form $4x-3y=k$, where k is a constant, represents a family of lines perpendicular to $3x+4y=6$ because we have satisfied the condition $AA' = - BB'$. Therefore, to find the specific line of the family containing (1, 2), we substitute 1 for x and 2 for y to determine k.
$4x-3y=k$
$4(1)- 3(2)=k$
$-2 = k$
Thus, the equation for the desired line is $4x-3y=-2$
Simplify $\dfrac{x}{{\sqrt {x + 4} }},\,\,x > 0$
Solve:
$2A - B = - 2C$
${A - B = - C}$
Find A and B.