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 444: 35

Answer

\[x=-5,\ y=-2\]

Work Step by Step

The equation \[2x=3y-4\]can be written as \[2x-3y=-4\]. Multiply \[3\]on both sides to the equation \[2x-3y=-4\]to get: \[6x-9y=-12\]. Add the above obtained equation from both RHS and LHS as follows: \[\underline{\begin{align} & 6x-9y=-12 \\ & -6x+12y=6 \end{align}}\] \[\begin{align} & \ \ \ \ \ \ \ \ \ 3y=-6 \\ & y=-2 \end{align}\] Put \[y=-2\]in\[2x-3y=-4\], to get: \[\begin{align} & 2x-3\left( -2 \right)=-4 \\ & 2x+6=-4 \\ & 2x=-10 \\ & x=-5 \end{align}\] Put\[x=-5\]and \[y=-2\]in any of the given equations to check the solution: \[\begin{align} & -6\left( -5 \right)+12\left( -2 \right)=6 \\ & 30-24=6 \\ & 6=6 \end{align}\] Since RHS\[=\]LHS, it implies the solution is correct. For complete verification, we have to put x = -5 and y = -2 in 2x = 3y – 4 too. 2(-5) = 3(-2) – 4 -10 = -6 – 4 -10 = - 10 LHS = RHS So, this is a solution to the above system of equations.
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