Use method of substitution to solve the system S 25y? – 16r?9y? – 4x² =36%3D

Answered: | 25у? — 16х? %3D 400 9y? – = 4x² 36

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter1: Foundations

Section: Chapter Questions

Problem 472PT: Convert (a) 511 to a decimal (b) 1.15 to a percent

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Use method of substitution to solve the system

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Step 1

$\begin{array}{l} We have \\ 25 y^{2} - 16 x^{2} = 400 ............ (1) \\ 9 y^{2} - 4 x^{2} = 36 ............. (2) \end{array}$

Step 2

$\begin{array}{l} Now \\ From equation (2) {find x}^{2} \\ 9 y^{2} - 36 = 4 x^{2} \\ \frac{9 y^{2} - 36}{4} = x^{2} \\ Put the value of x^{2} in equation (1) \\ 25 y^{2} - 16 x^{2} = 400 \\ 25 y^{2} - 16 (\frac{9 y^{2} - 36}{4}) = 400 \\ 25 y^{2} - 36 y^{2} + 144 = 400 \\ - 11 y^{2} = 256 \\ y^{2} = - \frac{256}{11} \\ Put y^{2} in equation x^{2} \\ \frac{9 y^{2} - 36}{4} = x^{2} \\ \frac{9 (- \frac{256}{11}) - 36}{4} = x^{2} \\ x^{2} = \frac{- 2304 - 396}{44} \\ x^{2} = - \frac{2700}{44} \end{array}$

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