Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 3 - Linear Systems - 3-2 Solving Systems Algebraically - Practice and Problem-Solving Exercises: 33

Answer

$a = 3$, $b = 2$, or $(3,2)$

Work Step by Step

Given: $2a + 3b = 12$ $5a - b = 13$ Multiply both sides of the second equation by $3$ to get an equivalent equation: $15a - 3b = 39$ Add the equations, $2a + 3b = 12$, and $15a - 3b = 39$: $2a + 3b + (15a - 3b) = 12 + (39) \\2a + 3b + 15a - 3b = 12 + 39$ Combine like terms: $17a = 51$ Divide both sides by $17$: $a = 3$ Substitute $a = 3$ back into first equation, $2a + 3b = 12$ : $2(3) + 3b = 12 \\6 + 3b = 12$ Subtract $6$ from both sides: $3b = 6$ Divide both sides by $3$: $b = 2$ Thus, $a = 3$, $b = 2$
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