Solve {l}{2=-3v+21}{v=3w+11}

$$\left. \begin{array} { l } { 2 = - 3 v + 21 } \\ { v = 3 w + 11 } \end{array} \right.$$

Solve for v, w

$$v = \frac{19}{3} = 6\frac{1}{3} \approx 6.333333333$$

$$w = -\frac{14}{9} = -1\frac{5}{9} \approx -1.555555556$$

Solution Steps

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

$$-3v+21=2$$

Subtract 21 from both sides.

$$-3v=2-21$$

Subtract 21 from 2 to get -19.

$$-3v=-19$$

Divide both sides by -3.

$$v=\frac{-19}{-3}$$

Fraction \frac{-19}{-3} can be simplified to \frac{19}{3} by removing the negative sign from both the numerator and the denominator.

$$v=\frac{19}{3}$$

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

$$\frac{19}{3}=3w+11$$

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

$$3w+11=\frac{19}{3}$$

Subtract 11 from both sides.

$$3w=\frac{19}{3}-11$$

Subtract 11 from \frac{19}{3} to get -\frac{14}{3}.

$$3w=-\frac{14}{3}$$

Divide both sides by 3.

$$w=\frac{-\frac{14}{3}}{3}$$

Express \frac{-\frac{14}{3}}{3} as a single fraction.

$$w=\frac{-14}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$w=\frac{-14}{9}$$

Fraction \frac{-14}{9} can be rewritten as -\frac{14}{9} by extracting the negative sign.

$$w=-\frac{14}{9}$$

The system is now solved.

$$v=\frac{19}{3} w=-\frac{14}{9}$$