Solve {l}{4y=2{(3y-1/2)}+1}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 4 y = 2 {(\frac{3 y - 1}{2})} + 1 }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, z, a

$$a=0$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 2.

$$8y=2\left(3y-1\right)+2$$

Use the distributive property to multiply 2 by 3y-1.

$$8y=6y-2+2$$

Add -2 and 2 to get 0.

$$8y=6y$$

Subtract 6y from both sides.

$$8y-6y=0$$

Combine 8y and -6y to get 2y.

$$2y=0$$

Divide both sides by 2. Zero divided by any non-zero number gives zero.

$$y=0$$

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

$$z=0$$

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

$$a=0$$

The system is now solved.

$$y=0 z=0 a=0$$