Consider the system of equations at right:   

1. What is the parent of each equation?

   Hint (a):

   Both equations are equations of lines.

2. Solve this system algebraically.

   Hint (b):

   Multiply the first equation by $−3$, then use elimination.
   Now substitute the value found for $x$ into the equation $3y−4x=−1$ and solve for $y$.

3. Find where the two graphs intersect.

   Hint (c):

   The graphs intersect at the solution to both equations.

4. Explain the relationship between parts (b) and (c) above.

   Hint (d):

   See part (c).

$\left. \begin{array} { l } { 3 y - 4 x = - 1 } \\ { 9 y + 2 x = 4 } \end{array} \right.$