Solve {l}{a-1+d=a+1}{a-1+2d=2a+3}

$$\left\{ \begin{array} { l } { a - 1 + d = a + 1 } \\ { a - 1 + 2 d = 2 a + 3 } \end{array} \right.$$

Solve for a, d

$$a=0$$

$$d=2$$

Solution Steps

Consider the first equation. Subtract a from both sides.

$$a-1+d-a=1$$

Combine a and -a to get 0.

$$-1+d=1$$

Add 1 to both sides.

$$d=1+1$$

Add 1 and 1 to get 2.

$$d=2$$

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

$$a-1+2\times 2=2a+3$$

Multiply 2 and 2 to get 4.

$$a-1+4=2a+3$$

Add -1 and 4 to get 3.

$$a+3=2a+3$$

Subtract 2a from both sides.

$$a+3-2a=3$$

Combine a and -2a to get -a.

$$-a+3=3$$

Subtract 3 from both sides.

$$-a=3-3$$

Subtract 3 from 3 to get 0.

$$-a=0$$

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$a=0$$

The system is now solved.

$$a=0 d=2$$