Solve {l}{3x+4y=5}{6y+5y=1}

$$\left\{ \begin{array} { l } { 3 x + 4 y = 5 } \\ { 6 y + 5 y = 1 } \end{array} \right.$$

Solve for x, y

$$x = \frac{17}{11} = 1\frac{6}{11} \approx 1.545454545$$

$$y=\frac{1}{11}\approx 0.090909091$$

Solution Steps

Consider the second equation. Combine 6y and 5y to get 11y.

$$11y=1$$

Divide both sides by 11.

$$y=\frac{1}{11}$$

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

$$3x+4\times \frac{1}{11}=5$$

Multiply 4 and \frac{1}{11} to get \frac{4}{11}.

$$3x+\frac{4}{11}=5$$

Subtract \frac{4}{11} from both sides.

$$3x=5-\frac{4}{11}$$

Subtract \frac{4}{11} from 5 to get \frac{51}{11}.

$$3x=\frac{51}{11}$$

Divide both sides by 3.

$$x=\frac{\frac{51}{11}}{3}$$

Express \frac{\frac{51}{11}}{3} as a single fraction.

$$x=\frac{51}{11\times 3}$$

Multiply 11 and 3 to get 33.

$$x=\frac{51}{33}$$

Reduce the fraction \frac{51}{33} to lowest terms by extracting and canceling out 3.

$$x=\frac{17}{11}$$

The system is now solved.

$$x=\frac{17}{11} y=\frac{1}{11}$$