Solve {l}{4x+3y-2b=43}{2x+9y=22}{14y-3x=0}

$$\left. \begin{array} { l } { 4 x + 3 y - 2 b = 43 } \\ { 2 x + 9 y = 22 } \\ { 14 y - 3 x = 0 } \end{array} \right.$$

Solve for x, y, b

$$x = \frac{28}{5} = 5\frac{3}{5} = 5.6$$

$$y = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

$$b = -\frac{17}{2} = -8\frac{1}{2} = -8.5$$

Short Steps Using Substitution

Solve 4x+3y-2b=43 for x.

$$x=-\frac{3}{4}y+\frac{1}{2}b+\frac{43}{4}$$

Substitute -\frac{3}{4}y+\frac{1}{2}b+\frac{43}{4} for x in the second and third equation.

$$2\left(-\frac{3}{4}y+\frac{1}{2}b+\frac{43}{4}\right)+9y=22 14y-3\left(-\frac{3}{4}y+\frac{1}{2}b+\frac{43}{4}\right)=0$$

Solve these equations for y and b respectively.

$$y=\frac{1}{15}-\frac{2}{15}b b=-\frac{43}{2}+\frac{65}{6}y$$

Substitute \frac{1}{15}-\frac{2}{15}b for y in the equation b=-\frac{43}{2}+\frac{65}{6}y.

$$b=-\frac{43}{2}+\frac{65}{6}\left(\frac{1}{15}-\frac{2}{15}b\right)$$

Solve b=-\frac{43}{2}+\frac{65}{6}\left(\frac{1}{15}-\frac{2}{15}b\right) for b.

$$b=-\frac{17}{2}$$

Substitute -\frac{17}{2} for b in the equation y=\frac{1}{15}-\frac{2}{15}b.

$$y=\frac{1}{15}-\frac{2}{15}\left(-\frac{17}{2}\right)$$

Calculate y from y=\frac{1}{15}-\frac{2}{15}\left(-\frac{17}{2}\right).

$$y=\frac{6}{5}$$

Substitute \frac{6}{5} for y and -\frac{17}{2} for b in the equation x=-\frac{3}{4}y+\frac{1}{2}b+\frac{43}{4}.

$$x=-\frac{3}{4}\times \frac{6}{5}+\frac{1}{2}\left(-\frac{17}{2}\right)+\frac{43}{4}$$

Calculate x from x=-\frac{3}{4}\times \frac{6}{5}+\frac{1}{2}\left(-\frac{17}{2}\right)+\frac{43}{4}.

$$x=\frac{28}{5}$$

The system is now solved.

$$x=\frac{28}{5} y=\frac{6}{5} b=-\frac{17}{2}$$