Solve {l}{2x/9+x/4=11}{5x/12+y/3=19}

$$\left. \begin{array} { l } { \frac { 2 x } { 9 } + \frac { x } { 4 } = 11 } \\ { \frac { 5 x } { 12 } + \frac { y } { 3 } = 19 } \end{array} \right.$$

Solve for x, y

$$x = \frac{396}{17} = 23\frac{5}{17} \approx 23.294117647$$

$$y = \frac{474}{17} = 27\frac{15}{17} \approx 27.882352941$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 36, the least common multiple of 9,4.

$$4\times 2x+9x=396$$

Multiply 4 and 2 to get 8.

$$8x+9x=396$$

Combine 8x and 9x to get 17x.

$$17x=396$$

Divide both sides by 17.

$$x=\frac{396}{17}$$

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

$$\frac{5\times \frac{396}{17}}{12}+\frac{y}{3}=19$$

Multiply both sides of the equation by 12, the least common multiple of 12,3.

$$5\times \frac{396}{17}+4y=228$$

Multiply 5 and \frac{396}{17} to get \frac{1980}{17}.

$$\frac{1980}{17}+4y=228$$

Subtract \frac{1980}{17} from both sides.

$$4y=228-\frac{1980}{17}$$

Subtract \frac{1980}{17} from 228 to get \frac{1896}{17}.

$$4y=\frac{1896}{17}$$

Divide both sides by 4.

$$y=\frac{\frac{1896}{17}}{4}$$

Express \frac{\frac{1896}{17}}{4} as a single fraction.

$$y=\frac{1896}{17\times 4}$$

Multiply 17 and 4 to get 68.

$$y=\frac{1896}{68}$$

Reduce the fraction \frac{1896}{68} to lowest terms by extracting and canceling out 4.

$$y=\frac{474}{17}$$

The system is now solved.

$$x=\frac{396}{17} y=\frac{474}{17}$$