Chapter 5.4, Problem 16E

To determine

To calculate:

System of linear equation.

Answer to Problem 16E

Solution for given linear equation is $x=3,y=7$

Explanation of Solution

Given information:

  $\begin{array}{l}3x-2y=-5\\ 4x+5y=47\end{array}$

Calculation:

Given equations are:

  $\begin{array}{l}3x-2y=-\mathrm{5...}\left(i\right)\\ 4x+5y=\mathrm{47...}\left(ii\right)\end{array}$

After simplifying,

  $3x-2y=-5$

Add $2y$ to both sides,

  $\begin{array}{l}3x-2y+2y=-5+2y\\ 3x=-5+2y\end{array}$

Divide both sides by $3$

  $\begin{array}{l}\frac{3x}{3}=\frac{-5}{3}+\frac{2y}{3}\\ x=\frac{-5}{3}+\frac{2y}{3}\end{array}$

Put $x=\frac{-5}{3}+\frac{2y}{3}$ in eq. $\left(ii\right)$

  $\begin{array}{l}4x+5y=47\\ 4\left(\frac{-5+2y}{3}\right)+5y=47\\ \frac{-20+23y}{3}=47\end{array}$

Now to find out $x$ put $y=7$ in $\frac{-20+23y}{3}=47$ and simplify,

Multiply by $3$

  $\begin{array}{l}\frac{3\left(-20+23y\right)}{3}=47.3\\ -20+23y=141\end{array}$

Add $20$ to both sides,

  $\begin{array}{l}-20+23y+20=141+20\\ 23y=161\end{array}$

Divide both sides by $23$ ,

  $\begin{array}{l}\frac{23y}{23}=\frac{161}{23}\\ y=7\end{array}$

Put $y=7$ in $x=\frac{-5}{3}+\frac{2y}{3}$

  $\begin{array}{l}x=\frac{-5+2.7}{3}\\ x=3\end{array}$

Hence solution fr given linear equation is $x=3,y=7$ .