Solve {l}{x/14+x/18=1}{x+y/2+3x-5y/4=2}

$$\left. \begin{array} { l } { \frac { x } { 14 } + \frac { x } { 18 } = 1 } \\ { \frac { x + y } { 2 } + \frac { 3 x - 5 y } { 4 } = 2 } \end{array} \right.$$

Solve for x, y

$$x = \frac{63}{8} = 7\frac{7}{8} = 7.875$$

$$y = \frac{251}{24} = 10\frac{11}{24} \approx 10.458333333$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 126, the least common multiple of 14,18.

$$9x+7x=126$$

Combine 9x and 7x to get 16x.

$$16x=126$$

Divide both sides by 16.

$$x=\frac{126}{16}$$

Reduce the fraction \frac{126}{16} to lowest terms by extracting and canceling out 2.

$$x=\frac{63}{8}$$

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

$$\frac{\frac{63}{8}+y}{2}+\frac{3\times \frac{63}{8}-5y}{4}=2$$

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(\frac{63}{8}+y\right)+3\times \frac{63}{8}-5y=8$$

Use the distributive property to multiply 2 by \frac{63}{8}+y.

$$\frac{63}{4}+2y+3\times \frac{63}{8}-5y=8$$

Multiply 3 and \frac{63}{8} to get \frac{189}{8}.

$$\frac{63}{4}+2y+\frac{189}{8}-5y=8$$

Add \frac{63}{4} and \frac{189}{8} to get \frac{315}{8}.

$$\frac{315}{8}+2y-5y=8$$

Combine 2y and -5y to get -3y.

$$\frac{315}{8}-3y=8$$

Subtract \frac{315}{8} from both sides.

$$-3y=8-\frac{315}{8}$$

Subtract \frac{315}{8} from 8 to get -\frac{251}{8}.

$$-3y=-\frac{251}{8}$$

Divide both sides by -3.

$$y=\frac{-\frac{251}{8}}{-3}$$

Express \frac{-\frac{251}{8}}{-3} as a single fraction.

$$y=\frac{-251}{8\left(-3\right)}$$

Multiply 8 and -3 to get -24.

$$y=\frac{-251}{-24}$$

Fraction \frac{-251}{-24} can be simplified to \frac{251}{24} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{251}{24}$$

The system is now solved.

$$x=\frac{63}{8} y=\frac{251}{24}$$