Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - 7.3 Systems of Linear Equations in Two Variables - Exercise Set 7.3 - Page 445: 41

Answer

The solution set is\[\left\{ \left( 1,4 \right) \right\}\].

Work Step by Step

Multiply \[2\]on both sides to the equation \[4x+y=8\]to get: \[8x+2y=16\]. Add the above obtained equation from both RHS and LHS as follows: \[\underline{\begin{align} & 3x-2y=-5 \\ & 8x+2y=16 \end{align}}\] \[\begin{align} & 11x\ \ \ \ \ \ \ =11 \\ & x=1 \end{align}\] Put \[x=1\]in\[3x-2y=-5\], to get: \[\begin{align} & 3\left( 1 \right)-2y=-5 \\ & 3-2y=-5 \\ & -2y=-8 \\ & y=4 \end{align}\] Put\[x=1\]and \[y=4\]in any of the given equations to check the solution: \[\begin{align} & 4\left( 1 \right)+4=8 \\ & 8=8 \end{align}\] Since RHS\[=\]LHS, it implies the solution is correct. We shall also check this solution with the equation 3x – 2y = -5 3(1) -2(4) = -5 3 – 8 = - 5 -5 = -5 So, this is the correct solution of the given system of equations.
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