Chapter 8, Problem 4CA

To determine

To Find: The classification for each system of equations by the number of solution.

Answer to Problem 4CA

The classification for each of the system is obtained.

Explanation of Solution

Consider given system of equation is,

  $\begin{array}{l}y=6x+9\\ y=-\frac{1}{6}x+9\end{array}$

The slope of both the equations shows that both the lines are perpendicular so the lines intersect at one point.

This shows that the number of solution is one.

Consider given system of equation is,

  $\begin{array}{l}7x+4y=12\\ -8y-12=-14x\end{array}$

Since, both the lines are parallel sot the number of solution is none.

Consider given system of equation is,

  $\begin{array}{l}2x+4y=-2\\ 10x+4y=-2\end{array}$

The lines are not parallel so they intersect at one point.

This shows that the number of solution is one.

Consider given system of equation is,

  $\begin{array}{l}3x+y=5\\ -15+3y+9x=0\end{array}$

Rewrite the equation as,

  $\begin{array}{l}y=-3x+5\\ y=5-3x\end{array}$

Since, both the lines are parallel sot the number of solution is none.

Consider given system of equation is,

  $\begin{array}{l}y-2x=\frac{3}{2}\\ -3+2y=4x\end{array}$

Rewrite the equation as,

  $\begin{array}{l}y=\frac{3}{2}+2x\\ y=2x+\frac{3}{2}\end{array}$

Since, both the lines are parallel sot the number of solution is none.

Consider given system of equation is,

  $\begin{array}{l}y=-3x+5\\ y=-3x+9\end{array}$

Since, both the lines are parallel sot the number of solution is none.