Solve {l}{x-(a+1)=3-a}{x+2(a+1)=5a}

$$\left\{ \begin{array} { l } { x - ( a + 1 ) = 3 - a } \\ { x + 2 ( a + 1 ) = 5 a } \end{array} \right.$$

Solve for x, a

$$x=4$$

$$a=2$$

Solution Steps

Consider the first equation. To find the opposite of a+1, find the opposite of each term.

$$x-a-1=3-a$$

Add a to both sides.

$$x-a-1+a=3$$

Combine -a and a to get 0.

$$x-1=3$$

Add 1 to both sides.

$$x=3+1$$

Add 3 and 1 to get 4.

$$x=4$$

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

$$4+2\left(a+1\right)=5a$$

Use the distributive property to multiply 2 by a+1.

$$4+2a+2=5a$$

Add 4 and 2 to get 6.

$$6+2a=5a$$

Subtract 5a from both sides.

$$6+2a-5a=0$$

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

$$6-3a=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-3a=-6$$

Divide both sides by -3.

$$a=\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$a=2$$

The system is now solved.

$$x=4 a=2$$