Solve {r}{-7x+6y=29}{10x+4=16}

$$\left. \begin{array} { r } { - 7 x + 6 y = 29 } \\ { 10 x + 4 = 16 } \end{array} \right.$$

Solve for x, y

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

$$y = \frac{187}{30} = 6\frac{7}{30} \approx 6.233333333$$

Solution Steps

Consider the second equation. Subtract 4 from both sides.

$$10x=16-4$$

Subtract 4 from 16 to get 12.

$$10x=12$$

Divide both sides by 10.

$$x=\frac{12}{10}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{6}{5}$$

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

$$-7\times \frac{6}{5}+6y=29$$

Multiply -7 and \frac{6}{5} to get -\frac{42}{5}.

$$-\frac{42}{5}+6y=29$$

Add \frac{42}{5} to both sides.

$$6y=29+\frac{42}{5}$$

Add 29 and \frac{42}{5} to get \frac{187}{5}.

$$6y=\frac{187}{5}$$

Divide both sides by 6.

$$y=\frac{\frac{187}{5}}{6}$$

Express \frac{\frac{187}{5}}{6} as a single fraction.

$$y=\frac{187}{5\times 6}$$

Multiply 5 and 6 to get 30.

$$y=\frac{187}{30}$$

The system is now solved.

$$x=\frac{6}{5} y=\frac{187}{30}$$