Solve the system of equation by the method of your choice.x^2+(y-9)^2=49, x^2-7y=-14

Tyra 2021-09-15 Answered
Solve the system of equation by the method of your choice.
\(\displaystyle{x}^{{2}}+{\left({y}-{9}\right)}^{{2}}={49}\)
\(\displaystyle{x}^{{2}}-{7}{y}=-{14}\)

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Expert Answer

grbavit
Answered 2021-09-16 Author has 16633 answers

Step 1
The system of equations is given by,
\(\displaystyle{x}^{{2}}+{\left({y}-{9}\right)}^{{2}}={49}\) (1)
\(\displaystyle{x}^{{2}}-{7}{y}=-{14}\) (2)
Step 2
Solve the system of equations.
\(\displaystyle{\left({7}{y}-{14}\right)}+{\left({y}-{9}\right)}^{{2}}={49}\)
\(\displaystyle{7}{y}-{14}+{y}^{{2}}-{18}{y}+{81}-{49}={0}\)
\(\displaystyle{y}^{{2}}-{11}{y}+{18}={0}\)
\(\displaystyle{y}^{{2}}-{9}{y}-{2}{y}+{18}={0}\)
\(\displaystyle{y}{\left({y}-{9}\right)}-{2}{\left({y}-{9}\right)}={0}\)
\(\displaystyle{\left({y}-{2}\right)}{\left({y}-{9}\right)}={0}\)
\(\displaystyle{y}={2},{9}\)
Step 3
The solution of the system of equations is computed as follows.
For y=2 , the value of x is \(\displaystyle{x}^{{2}}={7}{\left({2}\right)}-{14}\)
\(\displaystyle{x}^{{2}}={14}-{14}\)
\(\displaystyle{x}^{{2}}={0}\)
x=0
For y=9, the value of x is \(\displaystyle{x}^{{2}}={7}{\left({9}\right)}-{14}\)
\(\displaystyle{x}^{{2}}={63}-{14}\)
\(\displaystyle{x}^{{2}}={49}\)
\(\displaystyle{x}=\pm{7}\)
The solution is \( (0,2),(-7,9),(7,9)\)

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