Solve {l}{7x^{8}-4x+2+3x^8+x-5=10x^8-3}{y={(7x^8-4x+2)}-{(-3x^8-x+5)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 7 x ^ {8} - 4 x + 2 + 3 x ^ {8} + x - 5 = 10 x ^ {8} - 3 }\\ { y = {(7 x ^ {8} - 4 x + 2)} - {(-3 x ^ {8} - x + 5)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-3$$

Solution Steps

Consider the first equation. Combine 7x^{8} and 3x^{8} to get 10x^{8}.

$$10x^{8}-4x+2+x-5=10x^{8}-3$$

Combine -4x and x to get -3x.

$$10x^{8}-3x+2-5=10x^{8}-3$$

Subtract 5 from 2 to get -3.

$$10x^{8}-3x-3=10x^{8}-3$$

Subtract 10x^{8} from both sides.

$$10x^{8}-3x-3-10x^{8}=-3$$

Combine 10x^{8} and -10x^{8} to get 0.

$$-3x-3=-3$$

Add 3 to both sides.

$$-3x=-3+3$$

Add -3 and 3 to get 0.

$$-3x=0$$

Divide both sides by -3. Zero divided by any non-zero number gives zero.

$$x=0$$

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

$$y=7\times 0^{8}-4\times 0+2-\left(-3\times 0^{8}-0+5\right)$$

Calculate 0 to the power of 8 and get 0.

$$y=7\times 0-4\times 0+2-\left(-3\times 0^{8}-0+5\right)$$

Multiply 7 and 0 to get 0.

$$y=0-4\times 0+2-\left(-3\times 0^{8}-0+5\right)$$

Multiply -4 and 0 to get 0.

$$y=0+0+2-\left(-3\times 0^{8}-0+5\right)$$

Add 0 and 0 to get 0.

$$y=2-\left(-3\times 0^{8}-0+5\right)$$

Calculate 0 to the power of 8 and get 0.

$$y=2-\left(-3\times 0-0+5\right)$$

Multiply -3 and 0 to get 0.

$$y=2-\left(0-0+5\right)$$

Multiply -1 and 0 to get 0.

$$y=2-\left(0+0+5\right)$$

Add 0 and 0 to get 0.

$$y=2-5$$

Subtract 5 from 2 to get -3.

$$y=-3$$

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

$$z=-3$$

The system is now solved.

$$x=0 y=-3 z=-3$$