Solve {l}{5a+16=5}{2a+5b=9}

$$\left. \begin{array} { l } { 5 a + 16 = 5 } \\ { 2 a + 5 b = 9 } \end{array} \right.$$

Solve for a, b

$$a = -\frac{11}{5} = -2\frac{1}{5} = -2.2$$

$$b = \frac{67}{25} = 2\frac{17}{25} = 2.68$$

Solution Steps

Consider the first equation. Subtract 16 from both sides.

$$5a=5-16$$

Subtract 16 from 5 to get -11.

$$5a=-11$$

Divide both sides by 5.

$$a=-\frac{11}{5}$$

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

$$2\left(-\frac{11}{5}\right)+5b=9$$

Multiply 2 and -\frac{11}{5} to get -\frac{22}{5}.

$$-\frac{22}{5}+5b=9$$

Add \frac{22}{5} to both sides.

$$5b=9+\frac{22}{5}$$

Add 9 and \frac{22}{5} to get \frac{67}{5}.

$$5b=\frac{67}{5}$$

Divide both sides by 5.

$$b=\frac{\frac{67}{5}}{5}$$

Express \frac{\frac{67}{5}}{5} as a single fraction.

$$b=\frac{67}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$b=\frac{67}{25}$$

The system is now solved.

$$a=-\frac{11}{5} b=\frac{67}{25}$$