Solve {l}{4=3x+b}{2=6x+3}

$$\left\{ \begin{array} { l } { 4 = 3 x + b } \\ { 2 = 6 x + 3 } \end{array} \right.$$

Solve for x, b

$$x=-\frac{1}{6}\approx -0.166666667$$

$$b = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Solution Steps

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

$$6x+3=2$$

Subtract 3 from both sides.

$$6x=2-3$$

Subtract 3 from 2 to get -1.

$$6x=-1$$

Divide both sides by 6.

$$x=-\frac{1}{6}$$

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

$$4=3\left(-\frac{1}{6}\right)+b$$

Multiply 3 and -\frac{1}{6} to get -\frac{1}{2}.

$$4=-\frac{1}{2}+b$$

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

$$-\frac{1}{2}+b=4$$

Add \frac{1}{2} to both sides.

$$b=4+\frac{1}{2}$$

Add 4 and \frac{1}{2} to get \frac{9}{2}.

$$b=\frac{9}{2}$$

The system is now solved.

$$x=-\frac{1}{6} b=\frac{9}{2}$$