Chapter 5, Problem 2CT

To determine

To solve: Solve the system of linear equation using any method. And also to give the reasoning why did we use the respective method.

  $\frac{1}{2}x+y=-\mathrm{6...}\left(i\right)$

  $y=\frac{3}{5}x+\mathrm{5...}\left(ii\right)$

Answer to Problem 2CT

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

Explanation of Solution

Given information: The system of given equation is

  $\frac{1}{2}x+y=-\mathrm{6...}\left(i\right)$

  $y=\frac{3}{5}x+\mathrm{5...}\left(ii\right)$

Calculation: We use the method of elimination to solve

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

  $\frac{1}{2}x+\left(\frac{3}{5}x+5\right)=-6$

  $\frac{1}{2}x+\frac{3}{5}x=-11$

  $\frac{5x+6x}{10}=-11$

  $\frac{11x}{10}=-11$

  $x=\frac{-11*10}{11}$

  $x=-10$

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 already given the value of $y$ in equation $\left(ii\right)$ .