Solve {l}{2x-3/x+9=-1}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{2 x - 3}{x + 9} = -1 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-2$$

Solution Steps

Consider the first equation. Variable x cannot be equal to -9 since division by zero is not defined. Multiply both sides of the equation by x+9.

$$2x-3=-\left(x+9\right)$$

To find the opposite of x+9, find the opposite of each term.

$$2x-3=-x-9$$

Add x to both sides.

$$2x-3+x=-9$$

Combine 2x and x to get 3x.

$$3x-3=-9$$

Add 3 to both sides.

$$3x=-9+3$$

Add -9 and 3 to get -6.

$$3x=-6$$

Divide both sides by 3.

$$x=\frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$x=-2$$

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

$$y=-2$$

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

$$z=-2$$

The system is now solved.

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