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System of Equations Calculator
Solve system of equations
This solver (calculator) will try to solve a system of 2, 3, 4, 5 equations of any kind, including polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value, etc. It can find both the real and the complex solutions. To solve a system of linear equations with steps, use the system of linear equations calculator.
Your input: solve $$$\begin{cases} a + b + c + d=0 \\ 4 a - 7 b + c \left(-3 + 2 \sqrt{13}\right) + d \left(- 2 \sqrt{13} - 3\right)=3 \\ - 52 a - 52 b + c \left(-28 - 6 \sqrt{13}\right) + d \left(-28 + 6 \sqrt{13}\right)=-1 \\ - 208 a + 364 b - 56 \sqrt{13} c + 56 \sqrt{13} d=0 \end{cases}$$$ for $$$a$$$, $$$b$$$, $$$c$$$, $$$d$$$.
Answer
$$$a=- \frac{140}{33}\approx -4.24242424242424$$$, $$$b=\frac{13}{99}\approx 0.131313131313131$$$, $$$c=\frac{74 + 23 \sqrt{13}}{36}\approx 4.35910220376866$$$, $$$d=\frac{37}{18} - \frac{23 \sqrt{13}}{36}\approx -0.247991092657549$$$