Solve {l}{a=10}{b=-2}{c=6ab{(7a^2-b^2)}+7ab{(b^2-6a^2)}}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { a = 10 }\\ { b = -2 }\\ { c = 6 a b {(7 a ^ {2} - b ^ {2})} + 7 a b {(b ^ {2} - 6 a ^ {2})} }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Solve for a, b, c, d

$$d=-80$$

Solution Steps

Consider the third equation. Insert the known values of variables into the equation.

$$c=6\times 10\left(-2\right)\left(7\times 10^{2}-\left(-2\right)^{2}\right)+7\times 10\left(-2\right)\left(\left(-2\right)^{2}-6\times 10^{2}\right)$$

Do the multiplications.

$$c=60\left(-2\right)\left(7\times 10^{2}-\left(-2\right)^{2}\right)+70\left(-2\right)\left(\left(-2\right)^{2}-6\times 10^{2}\right)$$

Multiply 60 and -2 to get -120.

$$c=-120\left(7\times 10^{2}-\left(-2\right)^{2}\right)+70\left(-2\right)\left(\left(-2\right)^{2}-6\times 10^{2}\right)$$

Calculate 10 to the power of 2 and get 100.

$$c=-120\left(7\times 100-\left(-2\right)^{2}\right)+70\left(-2\right)\left(\left(-2\right)^{2}-6\times 10^{2}\right)$$

Multiply 7 and 100 to get 700.

$$c=-120\left(700-\left(-2\right)^{2}\right)+70\left(-2\right)\left(\left(-2\right)^{2}-6\times 10^{2}\right)$$

Calculate -2 to the power of 2 and get 4.

$$c=-120\left(700-4\right)+70\left(-2\right)\left(\left(-2\right)^{2}-6\times 10^{2}\right)$$

Subtract 4 from 700 to get 696.

$$c=-120\times 696+70\left(-2\right)\left(\left(-2\right)^{2}-6\times 10^{2}\right)$$

Multiply -120 and 696 to get -83520.

$$c=-83520+70\left(-2\right)\left(\left(-2\right)^{2}-6\times 10^{2}\right)$$

Multiply 70 and -2 to get -140.

$$c=-83520-140\left(\left(-2\right)^{2}-6\times 10^{2}\right)$$

Calculate -2 to the power of 2 and get 4.

$$c=-83520-140\left(4-6\times 10^{2}\right)$$

Calculate 10 to the power of 2 and get 100.

$$c=-83520-140\left(4-6\times 100\right)$$

Multiply -6 and 100 to get -600.

$$c=-83520-140\left(4-600\right)$$

Subtract 600 from 4 to get -596.

$$c=-83520-140\left(-596\right)$$

Multiply -140 and -596 to get 83440.

$$c=-83520+83440$$

Add -83520 and 83440 to get -80.

$$c=-80$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$d=-80$$

The system is now solved.

$$a=10 b=-2 c=-80 d=-80$$