Solve {l}{2^2+4^2=20s}{(7+10)^2+{(24x+1)}=537}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 2 ^ {2} + 4 ^ {2} = 20 s }\\ { {(7 + 10)} ^ {2} + {(24 x + 1)} = 537 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for s, x, y, z

$$z = \frac{247}{24} = 10\frac{7}{24} \approx 10.291666667$$

Solution Steps

Consider the first equation. Calculate 2 to the power of 2 and get 4.

$$4+4^{2}=20s$$

Calculate 4 to the power of 2 and get 16.

$$4+16=20s$$

Add 4 and 16 to get 20.

$$20=20s$$

Swap sides so that all variable terms are on the left hand side.

$$20s=20$$

Divide both sides by 20.

$$s=\frac{20}{20}$$

Divide 20 by 20 to get 1.

$$s=1$$

Consider the second equation. Add 7 and 10 to get 17.

$$17^{2}+24x+1=537$$

Calculate 17 to the power of 2 and get 289.

$$289+24x+1=537$$

Add 289 and 1 to get 290.

$$290+24x=537$$

Subtract 290 from both sides.

$$24x=537-290$$

Subtract 290 from 537 to get 247.

$$24x=247$$

Divide both sides by 24.

$$x=\frac{247}{24}$$

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

$$y=\frac{247}{24}$$

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

$$z=\frac{247}{24}$$

The system is now solved.

$$s=1 x=\frac{247}{24} y=\frac{247}{24} z=\frac{247}{24}$$