Solve {l}{x+y/6+x-y/6=4}{2x+y/4-2x-5y/3=5}

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

Solve for x, y

$$x=12$$

$$y = \frac{84}{23} = 3\frac{15}{23} \approx 3.652173913$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6.

$$x+y+x-y=24$$

Combine x and x to get 2x.

$$2x+y-y=24$$

Combine y and -y to get 0.

$$2x=24$$

Divide both sides by 2.

$$x=\frac{24}{2}$$

Divide 24 by 2 to get 12.

$$x=12$$

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

$$\frac{2\times 12+y}{4}-\frac{2\times 12-5y}{3}=5$$

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

$$3\left(2\times 12+y\right)-4\left(2\times 12-5y\right)=60$$

Multiply 2 and 12 to get 24.

$$3\left(24+y\right)-4\left(2\times 12-5y\right)=60$$

Use the distributive property to multiply 3 by 24+y.

$$72+3y-4\left(2\times 12-5y\right)=60$$

Multiply 2 and 12 to get 24.

$$72+3y-4\left(24-5y\right)=60$$

Use the distributive property to multiply -4 by 24-5y.

$$72+3y-96+20y=60$$

Subtract 96 from 72 to get -24.

$$-24+3y+20y=60$$

Combine 3y and 20y to get 23y.

$$-24+23y=60$$

Add 24 to both sides.

$$23y=60+24$$

Add 60 and 24 to get 84.

$$23y=84$$

Divide both sides by 23.

$$y=\frac{84}{23}$$

The system is now solved.

$$x=12 y=\frac{84}{23}$$