 # 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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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 $$(0,2),(-7,9),(7,9)$$