Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.4 - Systems of Nonlinear Equations in Two Variables - Concept and Vocabulary Check - Page 850: 3


The second equation is multiplied by $3$.

Work Step by Step

Let us consider the provided system: $\begin{align} & 3{{x}^{2}}+2{{y}^{2}}=35 \\ & 4{{x}^{2}}+3{{y}^{2}}=48 \end{align}$ And to eliminate ${{x}^{2}}$, multiply the first equation by $-4$ and the second equation by $3$ and add them to obtain, $\begin{align} & -12{{x}^{2}}-8{{y}^{2}}=-140 \\ & \underline{12{{x}^{2}}+9{{y}^{2}}=144} \\ & {{y}^{2}}=4 \\ \end{align}$ It gives the following values of y: $y=2,-2$ Thus, ${{x}^{2}}$ is eliminated on being multiplied by $3$ in the second equation.
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