Solve {l}{x-1/3+x+6/2=3}{x-2=3y-16}

$$\left\{ \begin{array} { l } { \frac { x - 1 } { 3 } + \frac { x + 6 } { 2 } = 3 } \\ { x - 2 = 3 y - 16 } \end{array} \right.$$

Solve for x, y

$$x=\frac{2}{5}=0.4$$

$$y = \frac{24}{5} = 4\frac{4}{5} = 4.8$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(x-1\right)+3\left(x+6\right)=18$$

Use the distributive property to multiply 2 by x-1.

$$2x-2+3\left(x+6\right)=18$$

Use the distributive property to multiply 3 by x+6.

$$2x-2+3x+18=18$$

Combine 2x and 3x to get 5x.

$$5x-2+18=18$$

Add -2 and 18 to get 16.

$$5x+16=18$$

Subtract 16 from both sides.

$$5x=18-16$$

Subtract 16 from 18 to get 2.

$$5x=2$$

Divide both sides by 5.

$$x=\frac{2}{5}$$

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

$$\frac{2}{5}-2=3y-16$$

Subtract 2 from \frac{2}{5} to get -\frac{8}{5}.

$$-\frac{8}{5}=3y-16$$

Swap sides so that all variable terms are on the left hand side.

$$3y-16=-\frac{8}{5}$$

Add 16 to both sides.

$$3y=-\frac{8}{5}+16$$

Add -\frac{8}{5} and 16 to get \frac{72}{5}.

$$3y=\frac{72}{5}$$

Divide both sides by 3.

$$y=\frac{\frac{72}{5}}{3}$$

Express \frac{\frac{72}{5}}{3} as a single fraction.

$$y=\frac{72}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$y=\frac{72}{15}$$

Reduce the fraction \frac{72}{15} to lowest terms by extracting and canceling out 3.

$$y=\frac{24}{5}$$

The system is now solved.

$$x=\frac{2}{5} y=\frac{24}{5}$$