Chapter 6.2, Problem 14PPS

To determine

To find: Values of x and y.

Answer to Problem 14PPS

There are infinitely many solutions

Explanation of Solution

Given information:

  $\begin{array}{l}y=-3x+4\\ -6x-2y=-8\end{array}$

$y=-3x+4$ -----(1)

$-6x-2y=-8$ ------(2)

Substitute the value of $y$ from equation-(1) in equation-(2)

We get

  $\begin{array}{l}-6x-2y=-8\\ \Rightarrow -6x-2\left(-3x+4\right)=-8\\ \Rightarrow -6x-2\left(-3x\right)-2\left(4\right)=-8\\ \Rightarrow -6x+6x-8=-8\\ \Rightarrow -8=-8\end{array}$

As this true.

So these lines are coincident lines.

Here one line can be written as factor of other line.

As

  $\begin{array}{l}-6x-2y=-8\\ \Rightarrow 2y=-6x+8\\ \Rightarrow 2y=2\left(-3x+4\right)\\ \Rightarrow y=-3x+4\end{array}$

So equation-(2) can be written as 2 multiplied by equation-(1)

So these two are coincident lines.

Therefore there are infinitely many solutions.