Chapter 6.2, Problem 5CYU

To determine

To find: Values of x and y.

Answer to Problem 5CYU

Infinitely many solutions.

Explanation of Solution

Given information:

  $\begin{array}{l}x-y=1\\ 3x=3y+3\end{array}$

  $x-y=1$

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

$3x=3y+3$ ------(2)

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

We get

  $\begin{array}{l}3x=3y+3\\ \Rightarrow 3\left(1+y\right)=3y+3\\ \Rightarrow 3\left(1\right)+3\left(y\right)=3y+3\\ \Rightarrow 3y+3=3y+3\\ \Rightarrow 0=0\end{array}$

So these lines are coincident lines.

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

As

Equation 2 can be written as

  $\begin{array}{l}3x=3y+3\\ \Rightarrow 3x-3y=3\\ \Rightarrow 3\left(x-y\right)=3\\ \Rightarrow x-y=1\end{array}$

Which is equation (1)

So equation-(2) can be written as 3 multiplied by equation-(1)

So these two are coincident lines.

Therefore there are infinitely many solutions.