Chapter 5, Problem 4CT

To determine

To solve: Solve the system of linear equation using any method. Explain why you chose the method.

  $x=y-11$

  $x-3y=1$

Answer to Problem 4CT

The solution of system of equations is $\left(-10,-1\right)$ . In the system of equations we can see that we are given the value of $x$ in equation $\left(i\right)$ .

Explanation of Solution

Given information: The system of given equation is

  $x=y-\mathrm{11...}(i)$

  $x-3y=\mathrm{1...}(ii)$

Calculation: We use the method of elimination to solve

From equation $\left(i\right)$ we know the value of $x$ in terms of $y$ , by putting this value in equation $(ii)$ , we get

  $\frac{1}{2}x+\frac{3}{5}x+5=-6$

  $\frac{5x+6x}{10}=-11$

  $11x=-110$

  $x=-10$

Now put value of $x$ in equation $\left(ii\right)$ to get the value of $y$

  $y=\frac{3}{5}\left(-10\right)+5$

  $y=-6+5$

  $y=-1$

Hence the solution of system of equations is $\left(-10,-1\right)$ .

In the system of equations we can see that we are given the value of $x$ in equation $\left(i\right)$ , so that we substitute it in another equation.