Chapter 9.4, Problem 29WE

To determine

To find: The value of $a$ & $b$ .

Answer to Problem 29WE

The value of $a$ is $4$ and $b$ is $-3$ .

Explanation of Solution

Given:

The given equations are as:

  $\begin{array}{c}ax+by=18\dots \left(1\right)\\ ax-by=6\dots \left(2\right)\end{array}$

The graphs of all the above equations intersect at the point $\left(3,-2\right)$

As any point of the equation satisfied that equation so by substituting the above intersecting point at the place of $x$ and $y$

in the given equations, the equations become as:

  $\begin{array}{c}3a-2b=18\dots \left(1\right)\\ 3a+2b=6\dots \left(2\right)\end{array}$

In order to find the value of $a$ and $b$ , solve the equation $\left(1\right)$ and $\left(2\right)$ by adding equation $\left(1\right)$ and $\left(2\right)$ then the solution is given as:

  $\begin{array}{c}3a-2b+\left(3a+2b\right)=18+6\\ 6a=24\\ a=4\end{array}$

Further simplified by substituting the value of $a=4$ in equation $\left(1\right)$, as:

  $\begin{array}{c}3\left(4\right)-2b=18\\ -2b=6\\ b=-3\end{array}$

So the value of $a$ is $4$ and $b$ is $-3$ .

So the graph of the above given equations is given as:

  

Therefore, the value of a is 4 and b is -3