Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 4 - Section 4.3 - Solving Systems of Linear Equations by the Addition Method - Exercise Set - Page 310: 3


The solution is $(3, 0)$.

Work Step by Step

The coefficients of the $y$ term differ only in sign, so if we add these equations without modification, we will cancel out the $y$ term and can then solve for $x$: Let us add the equations. First, we cancel out the $y$ term: $2x + 3y = 6$ $2x - 3y = 6$ _____________ $2x = 6$ $2x = 6$ Now we add both sides of the two equations to get: $$4x = 12$$ Divide by $4$ to solve for $x$: $$x = 3$$ Now that we have the value for $x$, we can plug this into one of the equations to solve for $y$. Let's use the first equation: $$2(3) + 3y = 6$$ Multiply: $$6 + 3y = 6$$ Subtract $6$ from both sides to isolate the variable on one side and constants on the other: $$3y = 0$$ Divide both sides by $3$ to solve for $y$: $$y = 0$$ The solution is $(3, 0)$.
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