Chapter 6, Problem 27SGR

To determine

To calculate:

The solution set of the given system of equations by elimination method:

  $\begin{array}{l}x+4y=-4\\ x+10y=-16\end{array}$

Answer to Problem 27SGR

The solution set of the given system of equations is $\left(4,-2\right)$

Explanation of Solution

Given information:

  $\begin{array}{l}x+4y=-4\\ x+10y=-16\end{array}$

Calculation:

The given system of equation is:

  $x+4y=-4$.........(1)

  $x+10y=-16$.........(2)

Take subtraction of both eqns.

  $\begin{array}{l}x+4y-x-10y=-4+16\\ -6y=12\\ y=-2\end{array}$

Calculate the value of $x$ by using the eq.(2):

  $\begin{array}{l}x+4y=-4\\ x+4\left(-2\right)=-4\\ x=4\end{array}$

The solution set of the given system of equations is $\left(x,y\right)=\left(4,-2\right)$