Solve {l}{7x+3y=10}{27+11x=2}

$$\left. \begin{array} { l } { 7 x + 3 y = 10 } \\ { 27 + 11 x = 2 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{25}{11} = -2\frac{3}{11} \approx -2.272727273$$

$$y = \frac{95}{11} = 8\frac{7}{11} \approx 8.636363636$$

Solution Steps

Consider the second equation. Subtract 27 from both sides.

$$11x=2-27$$

Subtract 27 from 2 to get -25.

$$11x=-25$$

Divide both sides by 11.

$$x=-\frac{25}{11}$$

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

$$7\left(-\frac{25}{11}\right)+3y=10$$

Multiply 7 and -\frac{25}{11} to get -\frac{175}{11}.

$$-\frac{175}{11}+3y=10$$

Add \frac{175}{11} to both sides.

$$3y=10+\frac{175}{11}$$

Add 10 and \frac{175}{11} to get \frac{285}{11}.

$$3y=\frac{285}{11}$$

Divide both sides by 3.

$$y=\frac{\frac{285}{11}}{3}$$

Express \frac{\frac{285}{11}}{3} as a single fraction.

$$y=\frac{285}{11\times 3}$$

Multiply 11 and 3 to get 33.

$$y=\frac{285}{33}$$

Reduce the fraction \frac{285}{33} to lowest terms by extracting and canceling out 3.

$$y=\frac{95}{11}$$

The system is now solved.

$$x=-\frac{25}{11} y=\frac{95}{11}$$