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

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

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 2,6.

$$3\left(1\times 5x+1\right)+0\times 2x=6$$

Multiply 1 and 5 to get 5.

$$3\left(5x+1\right)+0\times 2x=6$$

Use the distributive property to multiply 3 by 5x+1.

$$15x+3+0\times 2x=6$$

Multiply 0 and 2 to get 0.

$$15x+3+0x=6$$

Anything times zero gives zero.

$$15x+3+0=6$$

Add 3 and 0 to get 3.

$$15x+3=6$$

Subtract 3 from both sides.

$$15x=6-3$$

Subtract 3 from 6 to get 3.

$$15x=3$$

Divide both sides by 15.

$$x=\frac{3}{15}$$

Reduce the fraction \frac{3}{15} to lowest terms by extracting and canceling out 3.

$$x=\frac{1}{5}$$

The system is now solved.

$$x=\frac{1}{5} y=2 z=2$$