Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 3 - Section 3.1 - Systems of Two Equations in Two Unknowns - Exercises: 5

Answer

$(6,6)$

Work Step by Step

To eliminate y, multiply both equations with numbers so the coefficient of y is $\pm 6:$ $\left\{\begin{array}{llll} 3x & -2y & =6 & /\times 3\\ 2x & -3y & =-6 & /\times(-2) \end{array}\right.$ $\left\{\begin{array}{llll} 9x & -6y & =18 & \\ -4x & +6y & =12 & \end{array}\right.$ ... add and solve ... $5x=30\qquad/\div 5$ $x=6$ Back substitute into one of the initial equations: $3x-2y=6$ $3(6)-2y=6\qquad /-18$ $-2y=-12\qquad /\div(-2)$ $y=6$ Solutions are ordered pairs (x,y): $(6,6)$ Check graphically by graphing both lines in the same window and determining the intersection (see image).
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