## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Section 7.1 - Systems of Linear Equations in Two Variables - Exercise Set - Page 818: 51

#### Answer

The values of m and b are $-4$ and $3$ respectively.

#### Work Step by Step

We have the function $f\left( x \right)=mx+b$. To solve $f\left( -2 \right),$ put the value of $x=-2$ in the equation: $m\left( -2 \right)+b=11$ It gives: $-2m+b=11$ (I) Then solve $f\left( 3 \right),$ put the value of $x=3$ in the equation: $m\left( 3 \right)+b=-9$ It gives: $3m+b=-9$ (II) And subtract the equation (II) from equation (I): \begin{align} & -2m+b-\left( 3m+b \right)=11-\left( -9 \right) \\ & -2m+b-3m-b=11+9 \\ & -5m=20 \\ & m=-4 \end{align} Substitute the value of m in equation (I) and get: \begin{align} & -2\left( -4 \right)+b=11 \\ & 8+b=11 \\ & b=11-8 \\ & b=3 \end{align} Hence, the values of m and b are -4 and 3 respectively.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.