Solve {l}{6y-4=10y-20n}{6y-y/12=3y+184}

$$\left\{ \begin{array} { l } { 6 y - 4 = 10 y - 20 n } \\ { 6 y - \frac { y } { 12 } = 3 y + 184 } \end{array} \right.$$

Solve for y, n

$$y = \frac{2208}{35} = 63\frac{3}{35} \approx 63.085714286$$

$$n = \frac{2243}{175} = 12\frac{143}{175} \approx 12.817142857$$

Solution Steps

Consider the second equation. Multiply both sides of the equation by 12.

$$72y-y=36y+2208$$

Subtract 36y from both sides.

$$72y-y-36y=2208$$

Combine 72y and -36y to get 36y.

$$36y-y=2208$$

Combine 36y and -y to get 35y.

$$35y=2208$$

Divide both sides by 35.

$$y=\frac{2208}{35}$$

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

$$6\times \frac{2208}{35}-4=10\times \frac{2208}{35}-20n$$

Multiply 6 and \frac{2208}{35} to get \frac{13248}{35}.

$$\frac{13248}{35}-4=10\times \frac{2208}{35}-20n$$

Subtract 4 from \frac{13248}{35} to get \frac{13108}{35}.

$$\frac{13108}{35}=10\times \frac{2208}{35}-20n$$

Multiply 10 and \frac{2208}{35} to get \frac{4416}{7}.

$$\frac{13108}{35}=\frac{4416}{7}-20n$$

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

$$\frac{4416}{7}-20n=\frac{13108}{35}$$

Subtract \frac{4416}{7} from both sides.

$$-20n=\frac{13108}{35}-\frac{4416}{7}$$

Subtract \frac{4416}{7} from \frac{13108}{35} to get -\frac{8972}{35}.

$$-20n=-\frac{8972}{35}$$

Divide both sides by -20.

$$n=\frac{-\frac{8972}{35}}{-20}$$

Express \frac{-\frac{8972}{35}}{-20} as a single fraction.

$$n=\frac{-8972}{35\left(-20\right)}$$

Multiply 35 and -20 to get -700.

$$n=\frac{-8972}{-700}$$

Reduce the fraction \frac{-8972}{-700} to lowest terms by extracting and canceling out -4.

$$n=\frac{2243}{175}$$

The system is now solved.

$$y=\frac{2208}{35} n=\frac{2243}{175}$$