# The value of x and y for the following system of equations x^{2

The value of x and y for the following system of equations
$$\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={10}$$
$$\displaystyle{9}{x}^{{{2}}}+{y}^{{{2}}}={18}$$

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Step 1
1) $$\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={10}$$
2) $$\displaystyle{9}{x}^{{{2}}}+{y}^{{{2}}}={18}$$
Subtracting (1) from (2)
$$\displaystyle-{8}{x}^{{{2}}}=-{8}$$
$$\displaystyle{x}^{{{2}}}=-{1}$$
$$\displaystyle{x}=\pm{1}$$
Putting the value of x in (1)
$$\displaystyle{\left(\pm{1}\right)}^{{{2}}}+{y}^{{{2}}}={10}$$
$$\displaystyle{y}^{{{2}}}={10}-{1}$$
$$\displaystyle{y}^{{{2}}}={9}$$
$$\displaystyle{y}=\pm{3}$$