Chapter 9.2, Problem 37WE

To determine

To find: The value of $a\text{and}b$ for the equation intersecting at $\left(-2,3\right)$

Answer to Problem 37WE

The value of $a\text{and}b$ for the equation intersecting at $\left(-2,3\right)$ are $a=3$ and $b=-2$

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}ax+4y=6\\ x+by=-8\end{array}$

Intersection point is $\left(-2,3\right)$

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

For the given equation substitute -2 for $x$

  $\begin{array}{l}ax+4y=6\\ a\left(-2\right)+4\left(3\right)=6\\ -2a+12=6\\ -2a=-6\\ a=3\end{array}$

In another equation substitute 3 for $y$ and -2 for $x$

  $\begin{array}{l}x+by=-8\\ \left(-2\right)+b\left(3\right)=-8\\ -2+3b=-8\\ b=-2\end{array}$

Thus, The value of $a\text{and}b$ for the equation intersecting at $\left(-2,3\right)$ are $a=3$ and $b=-2$