Solve {l}{1-x/3+2x+1/2=1}{y=3x+1x-1}{text{Solvefor}ztext{where}}{z=y}

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

Solve for x, y, z

$$z=0$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(1-x\right)+3\left(2x+1\right)=6$$

Use the distributive property to multiply 2 by 1-x.

$$2-2x+3\left(2x+1\right)=6$$

Use the distributive property to multiply 3 by 2x+1.

$$2-2x+6x+3=6$$

Combine -2x and 6x to get 4x.

$$2+4x+3=6$$

Add 2 and 3 to get 5.

$$5+4x=6$$

Subtract 5 from both sides.

$$4x=6-5$$

Subtract 5 from 6 to get 1.

$$4x=1$$

Divide both sides by 4.

$$x=\frac{1}{4}$$

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

$$y=3\times \frac{1}{4}+1\times \frac{1}{4}-1$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$y=\frac{3}{4}+1\times \frac{1}{4}-1$$

Multiply 1 and \frac{1}{4} to get \frac{1}{4}.

$$y=\frac{3}{4}+\frac{1}{4}-1$$

Add \frac{3}{4} and \frac{1}{4} to get 1.

$$y=1-1$$

Subtract 1 from 1 to get 0.

$$y=0$$

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

$$z=0$$

The system is now solved.

$$x=\frac{1}{4} y=0 z=0$$