Chapter 6, Problem 38SGR

To determine

To calculate:

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

  $\begin{array}{l}8x-3y=-35\\ 3x+4y=33\end{array}$

Answer to Problem 38SGR

The solution set of the given system of equations is $\left(x,y\right)=\left(-1,9\right)$

Explanation of Solution

Given information:

  $\begin{array}{l}8x-3y=-35\\ 3x+4y=33\end{array}$

Calculation:

The given system of equation is:

  $8x-3y=-35$.........(1)

  $3x+4y=33$.........(2)

Solve $x$ for $8x-3y=-35$ ,

Put $x=\frac{-35+3y}{8}+4y=33$

After simplifying,

  $\frac{105+41y}{8}=33$

Now solve $y$ for $\frac{105+41y}{8}=33$ ,

  $x=\frac{-35+3\left(9\right)}{8}$

Put, $y=9$

  $\begin{array}{l}x=\frac{35+3\left(9\right)}{8}\\ x=-1\end{array}$

The solution set of the given system of equations is $\left(x,y\right)=\left(-1,9\right)$