Explanation Given information: The system of equations, 2 y = − 3 x − 6 9 x 2 + 4 y 2 = 36 Formula used: Steps for solving system of non-linear equations by substitution method as follows: Step 1: Simplify both equations if needed. Step 2: Solve one equation for either variable. Step 3: Substitute the value of one variable from step 2 into the other equation. Step 4: Solve for another variable. Step 5: Check the proposed order pair solution by substituting the value in original equations. Calculation: Consider the provided system of equations, 2 y = − 3 x − 6 9 x 2 + 4 y 2 = 36 Isolate first equation in one variable, Divide both sides by 2: 2 y 2 = 1 2 ( − 3 x − 6 ) y = 1 2 ( − 3 x − 6 ) Substitute this value of y in the second equation 9 x 2 + 4 y 2 = 36 : 9 x 2 + 4 ( 1 2 ( − 3 x − 6 ) ) 2 = 36 9 x 2 + 4 ( 1 4 ( − 3 x − 6 ) 2 ) = 36 9 x 2 + ( − 3 x − 6 ) 2 = 36 9 x 2 + 9 x 2 + 36 + 36 x = 36 Subtract 36 from both sides: 9 x 2 + 9 x 2 + 36 + 36 x − 36 = 36 − 36 18 x 2 + 36 x = 0 18 x ( x + 2 ) = 0 Here, 18 cannot be equal to 0, because 18 is a numerical constant. Thus, x ( x + 2 ) = 0 Now, apply zero product rule on above factors as: x = 0 or ( x + 2 ) = 0 If, ( x + 2 ) = 0 Then, x = − 2 Thus, x = 0 , x = − 2 , Now, to find the value of y , Substitute x = 0 in y = 1 2 ( − 3 x − 6 ) : y = 1 2 ( − 3 ( 0 ) − 6 ) y = 1 2 ( 0 − 6 ) y = 1 2 ( − 6 ) y = − 3 Substitute x = − 2 in y = 1 2 ( − 3 x − 6 ) : y = 1 2 ( − 3 ( − 2 ) − 6 ) y = 1 2 ( 6 − 6 ) y = 1 2 ( 0 ) y = 0 Thus, for x = 0 , y is − 3 and for x = − 2 , y is 0. Now, to check the solution of the system, Substitute x = 0 and y = − 3 in 2 y = − 3 x − 6 : 2 ( − 3 ) ? _ _ − 3 ( 0 ) − 6 − 6 ? _ _ − 6 As, both sides of above equations are same

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Chapter 13.4, Problem 35PE

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To calculate: The solution for the system, 2y=−3x−69x2+4y2=36 by using substitution method.

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Chapter 13.4, Problem 34PE

Chapter 13.4, Problem 36PE

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The solution for the system, 2 y = − 3 x − 6 9 x 2 + 4 y 2 = 36 by using substitution method.

Solution Summary: The author explains the steps for solving system of non-linear equations by using substitution method.

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To calculate: The solution for the system, 2y=−3x−69x2+4y2=36 by using substitution method.

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