Chapter 6.3, Problem 1P

To determine

To calculate: .Using substitution method

Answer to Problem 1P

a) $\begin{array}{l}x=2\\ y=7\end{array}$  b) $\begin{array}{l}x=-1\\ y=-2\end{array}$

Explanation of Solution

Given information:

  a) $\begin{array}{l}5x-6y=-32\\ 3x+6y=48\end{array}$  b) $\begin{array}{l}-3x-3y=9\\ 3x-4y=5\end{array}$

Calculation:

  a) $\begin{array}{l}5x-6y=-32\\ 3x+6y=48\end{array}$

Add the first equation with second on solving we get the value of x

  $\begin{array}{l}\Rightarrow 8x=16\\ x=\frac{16}{8}=2\end{array}$

now put the value of x in equation first to get the y value

  $\begin{array}{l}2\times 5-6y=-32\\ 10-6y=-32\\ 6y=32+10\\ y=\frac{42}{6}=7\end{array}$

  $\begin{array}{l}-3x-3y=9\\ 3x-4y=5\end{array}$

Add the first equation with second on solving we get the value of y

  $\begin{array}{l}\Rightarrow -7y=14\\ y=-\frac{14}{7}=-2\end{array}$

now put the value of y in equation first to get the x value

  $\begin{array}{l}-3x-3\times -2=9\\ -3x=9-6\\ -3x=3\\ x=-1\end{array}$

a)Add both of the linear equation and on solving the equation we get the value of x and then in the next step put the same value of x in either of the two equation to get the value of y, which is required.

b)Add both of the linear equation and on solving the equation we get the value of y and then in the next step put the same value of y in either of the two equation to get the value of x, which is required