Solve {l}{a=a+b+2}{0=16a+4b+2}

$$\left\{ \begin{array} { l } { a = a + b + 2 } \\ { 0 = 16 a + 4 b + 2 } \end{array} \right.$$

Solve for a, b

$$a=\frac{3}{8}=0.375$$

$$b=-2$$

Solution Steps

Consider the first equation. Subtract a from both sides.

$$a-a=b+2$$

Combine a and -a to get 0.

$$0=b+2$$

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

$$b+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$b=-2$$

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

$$0=16a+4\left(-2\right)+2$$

Multiply 4 and -2 to get -8.

$$0=16a-8+2$$

Add -8 and 2 to get -6.

$$0=16a-6$$

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

$$16a-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$16a=6$$

Divide both sides by 16.

$$a=\frac{6}{16}$$

Reduce the fraction \frac{6}{16} to lowest terms by extracting and canceling out 2.

$$a=\frac{3}{8}$$

The system is now solved.

$$a=\frac{3}{8} b=-2$$