Solve {l}{2z+5=11}{z/x-5=3}

$$\left. \begin{array} { l } { 2 z + 5 = 11 } \\ { \frac { z } { x } - 5 = 3 } \end{array} \right.$$

Solve for z, x

$$x=\frac{3}{8}=0.375$$

$$z=3$$

Solution Steps

Consider the first equation. Subtract 5 from both sides.

$$2z=11-5$$

Subtract 5 from 11 to get 6.

$$2z=6$$

Divide both sides by 2.

$$z=\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$z=3$$

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

$$\frac{3}{x}-5=3$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3+x\left(-5\right)=3x$$

Subtract 3x from both sides.

$$3+x\left(-5\right)-3x=0$$

Combine x\left(-5\right) and -3x to get -8x.

$$3-8x=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-8x=-3$$

Divide both sides by -8.

$$x=\frac{-3}{-8}$$

Fraction \frac{-3}{-8} can be simplified to \frac{3}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{3}{8}$$

The system is now solved.

$$z=3 x=\frac{3}{8}$$