Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 5 - Solving Systems of Linear Equations - 5.4 - Solving Special Systems of Linear Equations - Monitoring Progress - Page 255: 1

Answer

The system of linear equations has infinitely many solutions.

Work Step by Step

The given system of equations is $x+y=3$ ...... (1) $2x+2y=6$ ...... (2) Multiply equation (1) by $-2$. $-2(x+y)=-2(3)$ Use distributive property. $-2x-2y=-6$ ...... (3) Add equation (2) and (3). $\Rightarrow 2x+2y-2x-2y=6-6$ Add like terms. $\Rightarrow 0=0$ The equation $0=0$ is always true. Hence, the system of linear equations has infinitely many solutions.
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