Solve {l}{4x+9y=12}{3y-2z=1}{7x+5z=43/4}

$$\left. \begin{array} { l } { 4 x + 9 y = 12 } \\ { 3 y - 2 z = 1 } \\ { 7 x + 5 z = 4 \frac { 3 } { 4 } } \end{array} \right.$$

Solve for x, y, z

$$x=-\frac{3}{4}=-0.75$$

$$y = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$z=2$$

Short Steps Using Substitution

Multiply each equation by the least common multiple of denominators in it. Simplify.

$$4x+9y=12 3y-2z=1 28x+20z=19$$

Solve 4x+9y=12 for x.

$$x=3-\frac{9}{4}y$$

Substitute 3-\frac{9}{4}y for x in the equation 28x+20z=19.

$$28\left(3-\frac{9}{4}y\right)+20z=19$$

Solve the second equation for y and the third equation for z.

$$y=\frac{2}{3}z+\frac{1}{3} z=-\frac{13}{4}+\frac{63}{20}y$$

Substitute \frac{2}{3}z+\frac{1}{3} for y in the equation z=-\frac{13}{4}+\frac{63}{20}y.

$$z=-\frac{13}{4}+\frac{63}{20}\left(\frac{2}{3}z+\frac{1}{3}\right)$$

Solve z=-\frac{13}{4}+\frac{63}{20}\left(\frac{2}{3}z+\frac{1}{3}\right) for z.

$$z=2$$

Substitute 2 for z in the equation y=\frac{2}{3}z+\frac{1}{3}.

$$y=\frac{2}{3}\times 2+\frac{1}{3}$$

Calculate y from y=\frac{2}{3}\times 2+\frac{1}{3}.

$$y=\frac{5}{3}$$

Substitute \frac{5}{3} for y in the equation x=3-\frac{9}{4}y.

$$x=3-\frac{9}{4}\times \frac{5}{3}$$

Calculate x from x=3-\frac{9}{4}\times \frac{5}{3}.

$$x=-\frac{3}{4}$$

The system is now solved.

$$x=-\frac{3}{4} y=\frac{5}{3} z=2$$