Solve {r}{4x+5y-3z=-7}{y=5}{6y-5z=10}

$$\left. \begin{array} { r } { 4 x + 5 y - 3 z = - 7 } \\ { y = 5 } \\ { 6 y - 5 z = 10 } \end{array} \right.$$

Solve for x, y, z

$$x=-5$$

$$y=5$$

$$z=4$$

Solution Steps

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

$$6\times 5-5z=10$$

Multiply 6 and 5 to get 30.

$$30-5z=10$$

Subtract 30 from both sides.

$$-5z=10-30$$

Subtract 30 from 10 to get -20.

$$-5z=-20$$

Divide both sides by -5.

$$z=\frac{-20}{-5}$$

Divide -20 by -5 to get 4.

$$z=4$$

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

$$4x+5\times 5-3\times 4=-7$$

Do the multiplications.

$$4x+25-12=-7$$

Subtract 12 from 25 to get 13.

$$4x+13=-7$$

Subtract 13 from both sides.

$$4x=-7-13$$

Subtract 13 from -7 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.

$$x=-5 y=5 z=4$$