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: 20

Answer

\[\left\{ \left( 4,1 \right) \right\}\]

Work Step by Step

To find the solution of provided system of equation by substitution method use the following steps: Step1: The second equation, \[x-4y=0\], solve it for the x in terms of y. \[\begin{align} & x-4y=0 \\ & x=4y \end{align}\] Step2: Substitute the value of \[x=4y\] into the other equation\[2x+3y=11\]. The equation became in one variable y. Solve the equation for y. \[\begin{align} & 2x+3y=11 \\ & 2\left( 4y \right)+3y=11 \\ & 8y+3y=11 \\ & 11y=11 \end{align}\] Simplify the above equation: \[y=1\] Step3: Now, substitute the value of y obtained in step2, in \[x=4y\]. \[\begin{align} & x=4y \\ & x=4\cdot 1 \\ & x=4 \\ \end{align}\] Step4: The value of x and y obtained in step2 and step3, is the solution of the provided system of equations. Hence \[\left\{ \left( 4,1 \right) \right\}\]is the required solution. Step5: Now, to verify that the obtained solution is correct, substitute the values of x and y in both equations. Put \[x=4\text{ and }y=1\] \[\begin{align} & 2x+3y=11 \\ & 2\cdot 4+3\cdot 1=11 \\ & 8+3=11 \\ & 11=11 \end{align}\] \[\begin{align} & x-4y=0 \\ & 4-4\cdot 1=0 \\ & 4-4=0 \\ & 0=0 \end{align}\] Since, \[\left( 4,1 \right)\]satisfies both equations, the set \[\left( 4,1 \right)\]is the solution of the provided system of equations.
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