## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Section 7.1 - Systems of Linear Equations in Two Variables - Exercise Set - Page 818: 43

#### Answer

The system of equations modeling the word problem is $x+y=7$ and $x-y=-1$ and the solution to the system of equations is $\left( x,y \right)=\left( 3,4 \right)$.

#### Work Step by Step

Let us assume the two numbers are x and y. Sum of the numbers is 7. It gives the equation as: $x+y=7$ And the difference between the numbers is −1. It gives the equation as: $x-y=-1$ Add equations $x+y=7$ and $x-y=-1$ to obtain: \begin{align} & x+y+x-y=7-1 \\ & 2x=6 \\ & x=3 \end{align} Put the value of x in the equation $x+y=7$ to obtain: \begin{align} & 3+y=7 \\ & y=4 \end{align} Hence, thee systems of equations is $x+y=7$ and $x-y=-1$ and the solution of the equations is $\left( x,y \right)=\left( 3,4 \right)$.

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