Solve {l}{4x+1/5=2x-5/10-0}{y=6}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 4 x + \frac{1}{5} = \frac{2 x - 5}{10} - 0 }\\ { y = 6 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=6$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 10, the least common multiple of 5,10.

$$40x+2=2x-5-0$$

Subtract 2x-5 from both sides.

$$40x+2-\left(2x-5\right)=-0$$

To find the opposite of 2x-5, find the opposite of each term.

$$40x+2-2x+5=-0$$

Combine 40x and -2x to get 38x.

$$38x+2+5=-0$$

Add 2 and 5 to get 7.

$$38x+7=-0$$

Multiply -1 and 0 to get 0.

$$38x+7=0$$

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$38x=-7$$

Divide both sides by 38.

$$x=-\frac{7}{38}$$

The system is now solved.

$$x=-\frac{7}{38} y=6 z=6$$