Solve {l}{4n+5y=6}{4+7y=3}

$$\left. \begin{array} { l } { 4 n + 5 y = 6 } \\ { 4 + 7 y = 3 } \end{array} \right.$$

Solve for n, y

$$y=-\frac{1}{7}\approx -0.142857143$$

$$n = \frac{47}{28} = 1\frac{19}{28} \approx 1.678571429$$

Solution Steps

Consider the second equation. Subtract 4 from both sides.

$$7y=3-4$$

Subtract 4 from 3 to get -1.

$$7y=-1$$

Divide both sides by 7.

$$y=-\frac{1}{7}$$

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

$$4n+5\left(-\frac{1}{7}\right)=6$$

Multiply 5 and -\frac{1}{7} to get -\frac{5}{7}.

$$4n-\frac{5}{7}=6$$

Add \frac{5}{7} to both sides.

$$4n=6+\frac{5}{7}$$

Add 6 and \frac{5}{7} to get \frac{47}{7}.

$$4n=\frac{47}{7}$$

Divide both sides by 4.

$$n=\frac{\frac{47}{7}}{4}$$

Express \frac{\frac{47}{7}}{4} as a single fraction.

$$n=\frac{47}{7\times 4}$$

Multiply 7 and 4 to get 28.

$$n=\frac{47}{28}$$

The system is now solved.

$$n=\frac{47}{28} y=-\frac{1}{7}$$