To calculate: The solution for the system of equations 5x2+y2=14 and x2−2y2=−17. If the system does not have a unique solution, determine whether the system is inconsistent, or the equations are dependent.

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May Dunn · Accepted Answer

Calculation: Consider the provided system of equations: 5x2+y2=14.......(1) And, x2−2y2=−17.....(2) Multiply by 2 in equation (1) 10x2+2y2=28......(3) Add equations (3) and (2): 11x2=11 x2=1 x=±1 Now, substitute 1 for xin equation (2) and obtain the value of y: (1)2−2y2=−17 1−2y2=−17 −2y2=−18 y2=9 y=±3 Again, put x= and y=−3 in equation 5x2+y2=14: 5(1)2+(−3)2=?14 5+9=?14 14=?14 Put x=1 and y=—3 in equation x2−2y2=−17 (1)2−2(−3)2=?−17 1−18=?−17 −17=?−17 Again, put x=−1 and y=3 in equation 5x2+y2=14 5(−1)2+(3)2=?14 5+9=?14 14=?14 Put x=−1 and y=3 in equation x2−2y2=−17 (−1)2−2(3)2=?−17 1−18=?−17 −17=?−17 Again, put x=−1 and y=−3 in equation 5x2+y2=14 5(−1)2+(−3)2=?14 5+9=?14

To calculate: The solution for the system of equations 5x^{2}+y^{2}

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