Solve {l}{y=2x-1}{5x+3y+2z=2}{3x-4z=4}

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

Solve for y, x, z

$$x=\frac{14}{25}=0.56$$

$$y=\frac{3}{25}=0.12$$

$$z=-\frac{29}{50}=-0.58$$

Short Steps Using Substitution

Substitute 2x-1 for y in the equation 5x+3y+2z=2.

$$5x+3\left(2x-1\right)+2z=2$$

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

$$x=\frac{5}{11}-\frac{2}{11}z z=\frac{3}{4}x-1$$

Substitute \frac{5}{11}-\frac{2}{11}z for x in the equation z=\frac{3}{4}x-1.

$$z=\frac{3}{4}\left(\frac{5}{11}-\frac{2}{11}z\right)-1$$

Solve z=\frac{3}{4}\left(\frac{5}{11}-\frac{2}{11}z\right)-1 for z.

$$z=-\frac{29}{50}$$

Substitute -\frac{29}{50} for z in the equation x=\frac{5}{11}-\frac{2}{11}z.

$$x=\frac{5}{11}-\frac{2}{11}\left(-\frac{29}{50}\right)$$

Calculate x from x=\frac{5}{11}-\frac{2}{11}\left(-\frac{29}{50}\right).

$$x=\frac{14}{25}$$

Substitute \frac{14}{25} for x in the equation y=2x-1.

$$y=2\times \frac{14}{25}-1$$

Calculate y from y=2\times \frac{14}{25}-1.

$$y=\frac{3}{25}$$

The system is now solved.

$$y=\frac{3}{25} x=\frac{14}{25} z=-\frac{29}{50}$$