Solve {l}{x+2y=5}{y+2z=-1}{2z+5z=7}

$$\left\{ \begin{array} { l } { x + 2 y = 5 } \\ { y + 2 z = - 1 } \\ { 2 z + 5 z = 7 } \end{array} \right.$$

Solve for x, y, z

$$x=11$$

$$y=-3$$

$$z=1$$

Solution Steps

Consider the third equation. Combine 2z and 5z to get 7z.

$$7z=7$$

Divide both sides by 7.

$$z=\frac{7}{7}$$

Divide 7 by 7 to get 1.

$$z=1$$

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

$$y+2\times 1=-1$$

Multiply 2 and 1 to get 2.

$$y+2=-1$$

Subtract 2 from both sides.

$$y=-1-2$$

Subtract 2 from -1 to get -3.

$$y=-3$$

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

$$x+2\left(-3\right)=5$$

Multiply 2 and -3 to get -6.

$$x-6=5$$

Add 6 to both sides.

$$x=5+6$$

Add 5 and 6 to get 11.

$$x=11$$

The system is now solved.

$$x=11 y=-3 z=1$$