Solve {l}{-15x-6x={(-x+3)}-{(x+2)}+10}{y=9x}{z=y}{a=z}{b=a}{c=b}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { -15 x - 6 x = {(-x + 3)} - {(x + 2)} + 10 }\\ { y = 9 x }\\ { z = y }\\ { a = z }\\ { b = a }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Solve for x, y, z, a, b, c, d

$$d = -\frac{99}{19} = -5\frac{4}{19} \approx -5.210526316$$

Solution Steps

Consider the first equation. Combine -15x and -6x to get -21x.

$$-21x=-x+3-\left(x+2\right)+10$$

To find the opposite of x+2, find the opposite of each term.

$$-21x=-x+3-x-2+10$$

Subtract 2 from 3 to get 1.

$$-21x=-x+1-x+10$$

Add 1 and 10 to get 11.

$$-21x=-x+11-x$$

Add x to both sides.

$$-21x+x=11-x$$

Combine -21x and x to get -20x.

$$-20x=11-x$$

Add x to both sides.

$$-20x+x=11$$

Combine -20x and x to get -19x.

$$-19x=11$$

Divide both sides by -19.

$$x=-\frac{11}{19}$$

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

$$y=9\left(-\frac{11}{19}\right)$$

Multiply 9 and -\frac{11}{19} to get -\frac{99}{19}.

$$y=-\frac{99}{19}$$

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

$$z=-\frac{99}{19}$$

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

$$a=-\frac{99}{19}$$

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

$$b=-\frac{99}{19}$$

Consider the equation (6). Insert the known values of variables into the equation.

$$c=-\frac{99}{19}$$

Consider the equation (7). Insert the known values of variables into the equation.

$$d=-\frac{99}{19}$$

The system is now solved.

$$x=-\frac{11}{19} y=-\frac{99}{19} z=-\frac{99}{19} a=-\frac{99}{19} b=-\frac{99}{19} c=-\frac{99}{19} d=-\frac{99}{19}$$