Chapter 6, Problem 21CR

To determine

To solve the system of equations by using the method of elimination.

Answer to Problem 21CR

The solution is $x=-11,y=-7$ & the system of equation has one solution.

Explanation of Solution

Given information:

  $\begin{array}{l}5x+4y=-83\\ 3x-3y=-12\end{array}$

Calculation:

  $\begin{array}{l}5x+4y=-83\to \left(1\right)\\ 3x-3y=-12\to \left(2\right)\end{array}$

Now,

  $\begin{array}{l}\left[3\times \text{Equation}\left(\text{1}\right)\right]-\left[\text{5}\times \text{Equation}\left(\text{2}\right)\right]\\ 3\left(5x+4y\right)-5\left(3x-3y\right)=3\left(-83\right)-5\left(-12\right)\\ \Rightarrow 15x+12y-15x+15y=-249+60\\ \Rightarrow 27y=-189\\ \Rightarrow y=-7\end{array}$

Now put $y=-7$ in equation (1), we get

  $\begin{array}{l}5x+4\left(-7\right)=-83\\ \Rightarrow 5x-28=-83\\ \Rightarrow 5x=-55\\ \Rightarrow x=-11\end{array}$

Therefore the solution is $x=-11,y=-7$ & the system of equation has one solution.