Solve {l}{2x-10y=-5}{10y+6=8}{2x-5y+8z=9}

$$\left. \begin{array}{l}{ 2 x - 10 y = - 5 }\\{ 10 y + 6 = 8 }\\{ 2 x - 5 y + 8 z = 9 }\end{array} \right.$$

Solve for x, y, z

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$y=\frac{1}{5}=0.2$$

$$z=-\frac{t_{1744830465}}{8}+\frac{5}{4}$$

Solution Steps

Consider the second equation. Subtract 6 from both sides.

$$10y=8-6$$

Subtract 6 from 8 to get 2.

$$10y=2$$

Divide both sides by 10.

$$y=\frac{2}{10}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$y=\frac{1}{5}$$

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

$$2x-10\times \frac{1}{5}=-5$$

Multiply -10 and \frac{1}{5} to get -2.

$$2x-2=-5$$

Add 2 to both sides.

$$2x=-5+2$$

Add -5 and 2 to get -3.

$$2x=-3$$

Divide both sides by 2.

$$x=-\frac{3}{2}$$

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

$$2\left(-\frac{3}{2}\right)-5\times \frac{1}{5}+8z=9$$

Multiply 2 and -\frac{3}{2} to get -3.

$$-3-5\times \frac{1}{5}+8z=9$$

Multiply -5 and \frac{1}{5} to get -1.

$$-3-1+8z=9$$

Subtract 1 from -3 to get -4.

$$-4+8z=9$$

Add 4 to both sides.

$$8z=9+4$$

Add 9 and 4 to get 13.

$$8z=13$$

Divide both sides by 8.

$$z=\frac{13}{8}$$

The system is now solved.

$$x=-\frac{3}{2} y=\frac{1}{5} z=\frac{13}{8}$$