# Exercise ID302

Algebra → Quadratic equations, inequalities and systems of equations → Systems of Linear and Quadratic Equations
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Solve the following system of equations:

${x}^{2}+{y}^{2}=29x+y=7$

${x}^{2}+{y}^{2}=29x+y=7\phantom{\rule{0ex}{0ex}}$ $y=7-x\phantom{\rule{0ex}{0ex}}$ ${x}^{2}+{\left(7-x\right)}^{2}=29\phantom{\rule{0ex}{0ex}}$ ${x}^{2}+49-14x+{x}^{2}=29\phantom{\rule{0ex}{0ex}}$ ${x}^{2}+49-14x+{x}^{2}-29=0\phantom{\rule{0ex}{0ex}}$ $2{x}^{2}-14x+20=0|\frac{1}{2}\phantom{\rule{0ex}{0ex}}$ ${x}_{1,2}=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}=\frac{7±\sqrt{{7}^{2}-4·1·10}}{2}=\frac{7±\sqrt{49-40}}{2}=\frac{7±\sqrt{9}}{2}=\frac{7±3}{2}\phantom{\rule{0ex}{0ex}}$ ${{y}}_{1}{=}{7}{-}{{x}}_{1}{=}{7}{-}{5}{=}{2}\phantom{\rule{0ex}{0ex}}$ ${{y}}_{2}{=}{7}{-}{{x}}_{2}{=}{7}{-}{2}{=}{5}\phantom{\rule{0ex}{0ex}}$

${x}_{1,2}=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a};a{x}^{2}+bx+c=0$