Solve {l}{m+2n-1=5}{n+2+2n=3}

$$\left. \begin{array} { l } { m + 2 n - 1 = 5 } \\ { n + 2 + 2 n = 3 } \end{array} \right.$$

Solve for m, n

$$m = \frac{16}{3} = 5\frac{1}{3} \approx 5.333333333$$

$$n=\frac{1}{3}\approx 0.333333333$$

Solution Steps

Consider the second equation. Combine n and 2n to get 3n.

$$3n+2=3$$

Subtract 2 from both sides.

$$3n=3-2$$

Subtract 2 from 3 to get 1.

$$3n=1$$

Divide both sides by 3.

$$n=\frac{1}{3}$$

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

$$m+2\times \frac{1}{3}-1=5$$

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

$$m+\frac{2}{3}-1=5$$

Subtract 1 from \frac{2}{3} to get -\frac{1}{3}.

$$m-\frac{1}{3}=5$$

Add \frac{1}{3} to both sides.

$$m=5+\frac{1}{3}$$

Add 5 and \frac{1}{3} to get \frac{16}{3}.

$$m=\frac{16}{3}$$

The system is now solved.

$$m=\frac{16}{3} n=\frac{1}{3}$$