Solve {l}{2(x+5)=3x+1}{3y-4=6-2y}{3(n+2)=9(6-}

$$\left. \begin{array} { l } { 2 ( x + 5 ) = 3 x + 1 } \\ { 3 y - 4 = 6 - 2 y } \\ { 3 ( n + 2 ) = 9 ( 6 - } \end{array} \right.$$

Solve for x, y, n

$$x=9$$

$$y=2$$

$$n=1$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 2 by x+5.

$$2x+10=3x+1$$

Subtract 3x from both sides.

$$2x+10-3x=1$$

Combine 2x and -3x to get -x.

$$-x+10=1$$

Subtract 10 from both sides.

$$-x=1-10$$

Subtract 10 from 1 to get -9.

$$-x=-9$$

Divide both sides by -1.

$$x=\frac{-9}{-1}$$

Fraction \frac{-9}{-1} can be simplified to 9 by removing the negative sign from both the numerator and the denominator.

$$x=9$$

Consider the second equation. Add 2y to both sides.

$$3y-4+2y=6$$

Combine 3y and 2y to get 5y.

$$5y-4=6$$

Add 4 to both sides.

$$5y=6+4$$

Add 6 and 4 to get 10.

$$5y=10$$

Divide both sides by 5.

$$y=\frac{10}{5}$$

Divide 10 by 5 to get 2.

$$y=2$$

Consider the third equation. Divide both sides by 3.

$$n+2=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$n+2=3$$

Subtract 2 from both sides.

$$n=3-2$$

Subtract 2 from 3 to get 1.

$$n=1$$

The system is now solved.

$$x=9 y=2 n=1$$