Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 4 - Section 4.1 - Solving Systems of Linear Equations in Two Variables - Exercise Set - Page 212: 29

Answer

x=7 y=2 (7,2)

Work Step by Step

$3x-5y=11$ $2x-6y=2$ Equate the coefficients. Multiply the first equation by 2. $2(3x-5y)=2(11)\longrightarrow$ Simplify. Apply the distributive propety. $6x-10y=22$ Multiply the second equation by 3. $3(2x-6y)=3(2)\longrightarrow$ Simplify. Apply the distributive property. $6x-18y=6$ Subtract the new equations. $\ \ \ \ 6x-10y=22$ $\underline{-(6x-18y=6)}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8y=16$ Solve for y. $8y=16\longrightarrow$ Divide both sides by 8. $8y\div8=16\div8\longrightarrow$ Simplify. $y=2$ Substitute for y in one equation and solve for x. $3x-5(2)=11\longrightarrow$ Simplify. $3x-10=11\longrightarrow$ Add 10 to both sides. $3x-10+10=11+10\longrightarrow$ Simplify. $3x=21\longrightarrow$ Divide both sides by 3. $3x\div3=21\div3\longrightarrow$ Simplify. $x=7$
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