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

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

Solve for b, a

$$b=4$$

$$a=0$$

Solution Steps

Consider the first equation. Subtract a from both sides.

$$b-a=b$$

Subtract b from both sides.

$$b-a-b=0$$

Combine b and -b to get 0.

$$-a=0$$

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

$$a=0$$

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

$$4=2\times 0+b$$

Multiply 2 and 0 to get 0.

$$4=0+b$$

Anything plus zero gives itself.

$$4=b$$

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

$$b=4$$

The system is now solved.

$$b=4 a=0$$