Solve {l}{x+4y+2z=3}{5y+3z=4}{z=-2}

$$\left\{ \begin{array}{l}{ x + 4 y + 2 z = 3 }\\{ 5 y + 3 z = 4 }\\{ z = - 2 }\end{array} \right.$$

Solve for x, y, z

$$x=-1$$

$$y=2$$

$$z=-2$$

Solution Steps

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

$$5y+3\left(-2\right)=4$$

Multiply 3 and -2 to get -6.

$$5y-6=4$$

Add 6 to both sides.

$$5y=4+6$$

Add 4 and 6 to get 10.

$$5y=10$$

Divide both sides by 5.

$$y=\frac{10}{5}$$

Divide 10 by 5 to get 2.

$$y=2$$

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

$$x+4\times 2+2\left(-2\right)=3$$

Do the multiplications.

$$x+8-4=3$$

Subtract 4 from 8 to get 4.

$$x+4=3$$

Subtract 4 from both sides.

$$x=3-4$$

Subtract 4 from 3 to get -1.

$$x=-1$$

The system is now solved.

$$x=-1 y=2 z=-2$$