Solve {l}{v=-4+{(-1)}-{(5)}*{(-3)}-4+7*{(-2)}}{w=v-10-{(-1)}+{(-1)}*{(3)}-2*{(3)}+2}{x=w}{y=x}{z=y}{a=z}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { v = -4 + {(-1)} - {(5)} \cdot {(-3)} - 4 + 7 \cdot {(-2)} }\\ { w = v - 10 - {(-1)} + {(-1)} \cdot {(3)} - 2 \cdot {(3)} + 2 }\\ { x = w }\\ { y = x }\\ { z = y }\\ { a = z }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for v, w, x, y, z, a, b

$$b=-24$$

Solution Steps

Consider the first equation. Subtract 1 from -4 to get -5.

$$v=-5-5\left(-3\right)-4+7\left(-2\right)$$

Multiply 5 and -3 to get -15.

$$v=-5-\left(-15\right)-4+7\left(-2\right)$$

The opposite of -15 is 15.

$$v=-5+15-4+7\left(-2\right)$$

Add -5 and 15 to get 10.

$$v=10-4+7\left(-2\right)$$

Subtract 4 from 10 to get 6.

$$v=6+7\left(-2\right)$$

Multiply 7 and -2 to get -14.

$$v=6-14$$

Subtract 14 from 6 to get -8.

$$v=-8$$

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

$$w=-8-10-\left(-1\right)-3-2\times 3+2$$

Subtract 10 from -8 to get -18.

$$w=-18-\left(-1\right)-3-2\times 3+2$$

The opposite of -1 is 1.

$$w=-18+1-3-2\times 3+2$$

Add -18 and 1 to get -17.

$$w=-17-3-2\times 3+2$$

Subtract 3 from -17 to get -20.

$$w=-20-2\times 3+2$$

Multiply 2 and 3 to get 6.

$$w=-20-6+2$$

Subtract 6 from -20 to get -26.

$$w=-26+2$$

Add -26 and 2 to get -24.

$$w=-24$$

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

$$x=-24$$

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

$$y=-24$$

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

$$z=-24$$

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

$$a=-24$$

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

$$b=-24$$

The system is now solved.

$$v=-8 w=-24 x=-24 y=-24 z=-24 a=-24 b=-24$$