Solve {l}{03x+5y=29}{-x-4y=16}

$$\left. \begin{array} { l } { 03 x + 5 y = 29 } \\ { - x - 4 y = 16 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{196}{5} = -39\frac{1}{5} = -39.2$$

$$y = \frac{29}{5} = 5\frac{4}{5} = 5.8$$

Solution Steps

Consider the first equation. Multiply 0 and 3 to get 0.

$$0x+5y=29$$

Anything times zero gives zero.

$$0+5y=29$$

Anything plus zero gives itself.

$$5y=29$$

Divide both sides by 5.

$$y=\frac{29}{5}$$

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

$$-x-4\times \frac{29}{5}=16$$

Multiply -4 and \frac{29}{5} to get -\frac{116}{5}.

$$-x-\frac{116}{5}=16$$

Add \frac{116}{5} to both sides.

$$-x=16+\frac{116}{5}$$

Add 16 and \frac{116}{5} to get \frac{196}{5}.

$$-x=\frac{196}{5}$$

Divide both sides by -1.

$$x=\frac{\frac{196}{5}}{-1}$$

Express \frac{\frac{196}{5}}{-1} as a single fraction.

$$x=\frac{196}{5\left(-1\right)}$$

Multiply 5 and -1 to get -5.

$$x=\frac{196}{-5}$$

Fraction \frac{196}{-5} can be rewritten as -\frac{196}{5} by extracting the negative sign.

$$x=-\frac{196}{5}$$

The system is now solved.

$$x=-\frac{196}{5} y=\frac{29}{5}$$