Solve {l}{x+2+z=73}{x+2x-2=7}{3x-y+z=23}

$$\left\{ \begin{array} { l } { x + 2 + z = 73 } \\ { x + 2 x - 2 = 7 } \\ { 3 x - y + z = 23 } \end{array} \right.$$

Solve for x, z, y

$$x=3$$

$$y=54$$

$$z=68$$

Solution Steps

Consider the second equation. Combine x and 2x to get 3x.

$$3x-2=7$$

Add 2 to both sides.

$$3x=7+2$$

Add 7 and 2 to get 9.

$$3x=9$$

Divide both sides by 3.

$$x=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$x=3$$

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

$$3+2+z=73$$

Add 3 and 2 to get 5.

$$5+z=73$$

Subtract 5 from both sides.

$$z=73-5$$

Subtract 5 from 73 to get 68.

$$z=68$$

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

$$3\times 3-y+68=23$$

Multiply 3 and 3 to get 9.

$$9-y+68=23$$

Add 9 and 68 to get 77.

$$77-y=23$$

Subtract 77 from both sides.

$$-y=23-77$$

Subtract 77 from 23 to get -54.

$$-y=-54$$

Divide both sides by -1.

$$y=\frac{-54}{-1}$$

Fraction \frac{-54}{-1} can be simplified to 54 by removing the negative sign from both the numerator and the denominator.

$$y=54$$

The system is now solved.

$$x=3 z=68 y=54$$