Solve {l}{2x/3+3x/4=1/2}{4x/5+frac{5y}{6}=frac{7}{15}}

$$\left\{ \begin{array} { l } { \frac { 2 x } { 3 } + \frac { 3 x } { 4 } = \frac { 1 } { 2 } } \\ { \frac { 4 x } { 5 } + \frac { 5 y } { 6 } = \frac { 7 } { 15 } } \end{array} \right.$$

Solve for x, y

$$x=\frac{6}{17}\approx 0.352941176$$

$$y=\frac{94}{425}\approx 0.221176471$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 12, the least common multiple of 3,4,2.

$$4\times 2x+3\times 3x=6$$

Multiply 4 and 2 to get 8.

$$8x+3\times 3x=6$$

Multiply 3 and 3 to get 9.

$$8x+9x=6$$

Combine 8x and 9x to get 17x.

$$17x=6$$

Divide both sides by 17.

$$x=\frac{6}{17}$$

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

$$\frac{4\times \frac{6}{17}}{5}+\frac{5y}{6}=\frac{7}{15}$$

Multiply both sides of the equation by 30, the least common multiple of 5,6,15.

$$6\times 4\times \frac{6}{17}+5\times 5y=14$$

Multiply 6 and 4 to get 24.

$$24\times \frac{6}{17}+5\times 5y=14$$

Multiply 24 and \frac{6}{17} to get \frac{144}{17}.

$$\frac{144}{17}+5\times 5y=14$$

Multiply 5 and 5 to get 25.

$$\frac{144}{17}+25y=14$$

Subtract \frac{144}{17} from both sides.

$$25y=14-\frac{144}{17}$$

Subtract \frac{144}{17} from 14 to get \frac{94}{17}.

$$25y=\frac{94}{17}$$

Divide both sides by 25.

$$y=\frac{\frac{94}{17}}{25}$$

Express \frac{\frac{94}{17}}{25} as a single fraction.

$$y=\frac{94}{17\times 25}$$

Multiply 17 and 25 to get 425.

$$y=\frac{94}{425}$$

The system is now solved.

$$x=\frac{6}{17} y=\frac{94}{425}$$