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

signokodo7h 2021-11-12 Answered
To calculate: The solution for the system of equations 5x2+y2=14 and x22y2=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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Expert Answer

May Dunn
Answered 2021-11-13 Author has 12 answers

Calculation:
Consider the provided system of equations:
5x2+y2=14.......(1)
And,
x22y2=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)22y2=17
12y2=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 x22y2=17
(1)22(3)2=?17
118=?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 x22y2=17
(1)22(3)2=?17
118=?17
17=?17
Again, put x=1 and y=3 in equation 5x2+y2=14
5(1)2+(3)2=?14
5+9=?14

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