Chapter SH, Problem 6.3.5EP

To determine

The solution of the given equations.

Answer to Problem 6.3.5EP

The solution is $\left(-11,-4\right)$

Explanation of Solution

Given:

The given equations are:

  $\begin{array}{l}x=y-\mathrm{7......................}\left(1\right)\\ \text{and}\\ 2x-5y=-\mathrm{2............................}\left(2\right)\end{array}$

Calculation:

Multiply equation 1 with 2 and change the sign as:

  $\begin{array}{l}2\left(x\right)=2\left(y-7\right)\\ 2x-2y=-14\\ -2x+2y=\mathrm{14....................}\left(3\right)\end{array}$

Add equations 3 and 2,

  $\begin{array}{l}2x-5y-2x+2y=14-2\\ -3y=12\\ y=-4\end{array}$

Put the value of y in equation 1,

  $\begin{array}{l}x=y-7\\ x=-4-7\\ x=-11\end{array}$

Hence, the solution is $\left(-11,-4\right)$