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: 42

Answer

$m = 1$, $n = -4$

Work Step by Step

Given: $3m + 4n = -13$ $5m + 6n = -19$ Multiply both sides of the first equation, $3m + 4n = -13$, by $3$: $9m + 12n = -39$ Multiply both sides of the second equation, $5m + 6n = -19$ by $2$: $10m + 12n = -38$ Subtract the first equation, $9m + 12n = -39$, from the second equation, $10m + 12n = -38$: $10m + 12n - (9m + 12n) = -38 - (-39)$ $10m + 12n - (9m + 12n) = -38 + 39$ $10m + 12n - (9m + 12n) = 1$ Subtract each term of the binomial: $10m - 9m + 12n - 12n = 1$ Combine like terms: $m = 1$ Substitute $m = 1$ into the original first equation, $3m + 4n = -13$: $3m + 4n = -13$: $3(1) + 4n = -13$ $3 + 4n = -13$ Subtract $3$ from both sides: $4n = -16$ Divide both sides by $4$: $n = -4$ $m = 1$, $n = -4$
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