To calculate: The solution for the system of equations −2x2+3y2=10; 5x2+2y2=13.

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To calculate: The solution for the system of equations  −2x2+3y2=10;   5x2+2y2=13.

Roger Noah · Accepted Answer

Given Information:    The provided system of equations is:    −2x2+3y2=10    5x2+2y2=13    Calculation:    Consider the provided system of equations:    A.−2x2+3y2=10    B. 5x2+2y2=13    Multiply A with 5 and B with 2:    5⋅A−10x2+15y2=50    2⋅B10x2+4y2=26    Add both the above equations:    19y2=76    Dividing both sides by 19,    y2=4    y=±2    Now, substitute 2 for y in B and obtain the value of x:    5x2+2(2)2=13    5x2+8=13    Subtracting 8 from both sides then dividing by 5,    5x2=5    x2=1    x=±1  Now, substitute —2 for y in B and obtain the value of x:    5x2+2(−2)2=13    5x2+8=13    Subtracting 8 from both sides then dividing by 5,    5x2=5    x2=1    x=±1    So, the solutions sets obtained are    {(1,2),(1,−2),(−1,2),(−1,−2)}.    Therefore, the solutions to the set of equations  −2x2+3y2=10; 5x2+2y2=13 is    {(1,2),(1,−2),(−1,2),(−1,−2)}.

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

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