Solve {l}{5y+2z=7}{2y=-2}{4x+6y+5z=4}

$$\left\{ \begin{array}{l}{ 5 y + 2 z = 7 }\\{ 2 y = - 2 }\\{ 4 x + 6 y + 5 z = 4 }\end{array} \right.$$

Solve for y, z, x

$$x=-5$$

$$y=-1$$

$$z=6$$

Solution Steps

Consider the second equation. Divide both sides by 2.

$$y=\frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$y=-1$$

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

$$5\left(-1\right)+2z=7$$

Multiply 5 and -1 to get -5.

$$-5+2z=7$$

Add 5 to both sides.

$$2z=7+5$$

Add 7 and 5 to get 12.

$$2z=12$$

Divide both sides by 2.

$$z=\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$z=6$$

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

$$4x+6\left(-1\right)+5\times 6=4$$

Do the multiplications.

$$4x-6+30=4$$

Add -6 and 30 to get 24.

$$4x+24=4$$

Subtract 24 from both sides.

$$4x=4-24$$

Subtract 24 from 4 to get -20.

$$4x=-20$$

Divide both sides by 4.

$$x=\frac{-20}{4}$$

Divide -20 by 4 to get -5.

$$x=-5$$

The system is now solved.

$$y=-1 z=6 x=-5$$