Chapter 5.4, Problem 7Q

To determine

To find: The solution of the linear equations $x+y=4\text{ and }-3x-y=-8$ and also check the solution.

Answer to Problem 7Q

The solution ofgiven equations $x+y=4\text{ and }-3x-y=-8$ is $\left(2,2\right)$.

Explanation of Solution

Given information:

The system of linear equations is as follows:

  $x+y=4\text{ and }-3x-y=-8$

Calculation:

The given system of linear equations is as follows:

  $x+y=4$   ...... (1)

  $-3x-y=-8$   ...... (2)

Add the equation (1) and equation (2) to obtain the value of $x$ .

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

Now, put the value of $x$ in the equation (1) to obtain the value of $y$ .

  $\begin{array}{c}2+y=4\\ y=4-2\\ y=2\end{array}$

Check whether the resultant point $\left(2,2\right)$ is the solution of the given system of equation or not.

Substitute, the $2\text{ for }x$ and $2\text{ for }y$ in the equation (1).

  $\begin{array}{r}x+y=4\\ 2+2\stackrel{?}{=}4\\ 4=4\end{array}$

Substitute, the $2\text{ for }x$ and $2\text{ for }y$ in the equation (2).

  $\begin{array}{r}-3x-y=-8\\ -3\left(2\right)-2\stackrel{?}{=}-8\\ -6-2\stackrel{?}{=}-8\\ -8=-8\end{array}$

Therefore, it can be seen that point $\left(2,2\right)$ satisfies the solution of given system of equations.

Conclusion Thus, the solution of the given system of equation is $\left(2,2\right)$ .