Chapter 9.2, Problem 38WE

To determine

To find: The value of $a\text{and}b$ for the equation intersecting at $\left(1,4\right)$

Answer to Problem 38WE

The value of $a\text{and}b$ for the equation intersecting at $\left(1,4\right)$ are $a=5$ and $b=2$

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}ax+by=13\\ ax-by=-3\end{array}$

Intersection point is $\left(1,4\right)$

The given equation can be substituted with the given intersection point as it will be solution of the equation:

For the given equation substitute 1 for $x$ and 4 for $y$

  $\begin{array}{l}ax+by=13\\ \left(1\right)a+\left(4\right)b=13\\ a+4b=13\end{array}$ ................. (1)

In another equation substitute 1 for $x$ and 4 for $y$

  $\begin{array}{l}ax-by=-3\\ \left(1\right)a-\left(4\right)b=-3\\ a-4b=-3\end{array}$ ................. (2)

Adding both the Equations:

  $\begin{array}{l}a+4b+a-4b=13-3\\ 2a=10\\ a=5\end{array}$

Substitute 5 for $a$ in Equation (1):

  $\begin{array}{l}a+4b=13\\ 5+4b=13\\ 4b=13-5\\ b=2\end{array}$

Thus, The value of $a\text{and}b$ for the equation intersecting at $\left(1,4\right)$ are $a=5$ and $b=2$