Solve {l}{x=6+1}{y=-2+{(-1)}}{0=-4+1-2t}{u=5t}{v=5t}{text{Solvefor}w,ztext{where}}{w=u}{z=v}

$$\left. \begin{array} { l } { x = 6 + 1 }\\ { y = -2 + {(-1)} }\\ { 0 = -4 + 1 - 2 t }\\ { u = 5 t }\\ { v = 5 t }\\ { \text{Solve for } w,z \text{ where} } \\ { w = u }\\ { z = v } \end{array} \right.$$

Solve for x, y, t, u, v, w, z

$$z = -\frac{15}{2} = -7\frac{1}{2} = -7.5$$

$$w = -\frac{15}{2} = -7\frac{1}{2} = -7.5$$

Solution Steps

Consider the first equation. Add 6 and 1 to get 7.

$$x=7$$

Consider the second equation. Subtract 1 from -2 to get -3.

$$y=-3$$

Consider the third equation. Add -4 and 1 to get -3.

$$0=-3-2t$$

Swap sides so that all variable terms are on the left hand side.

$$-3-2t=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$-2t=3$$

Divide both sides by -2.

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

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

$$u=5\left(-\frac{3}{2}\right)$$

Multiply 5 and -\frac{3}{2} to get -\frac{15}{2}.

$$u=-\frac{15}{2}$$

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

$$v=5\left(-\frac{3}{2}\right)$$

Multiply 5 and -\frac{3}{2} to get -\frac{15}{2}.

$$v=-\frac{15}{2}$$

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

$$w=-\frac{15}{2}$$

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

$$z=-\frac{15}{2}$$

The system is now solved.

$$x=7 y=-3 t=-\frac{3}{2} u=-\frac{15}{2} v=-\frac{15}{2} w=-\frac{15}{2} z=-\frac{15}{2}$$