Solve {l}{x+6y=20}{5x-4y-5m=-27}{3x-2y+1m-35=0}

$$\left. \begin{array} { l } { x + 6 y = 20 } \\ { 5 x - 4 y - 5 m = - 27 } \\ { 3 x - 2 y + 1 m - 35 = 0 } \end{array} \right.$$

Solve for x, y, m

$$x = \frac{584}{67} = 8\frac{48}{67} \approx 8.71641791$$

$$y = \frac{126}{67} = 1\frac{59}{67} \approx 1.880597015$$

$$m = \frac{845}{67} = 12\frac{41}{67} \approx 12.611940299$$

Short Steps Using Substitution

Solve x+6y=20 for x.

$$x=20-6y$$

Substitute 20-6y for x in the second and third equation.

$$5\left(20-6y\right)-4y-5m=-27 3\left(20-6y\right)-2y+1m-35=0$$

Solve these equations for y and m respectively.

$$y=\frac{127}{34}-\frac{5}{34}m m=-25+20y$$

Substitute \frac{127}{34}-\frac{5}{34}m for y in the equation m=-25+20y.

$$m=-25+20\left(\frac{127}{34}-\frac{5}{34}m\right)$$

Solve m=-25+20\left(\frac{127}{34}-\frac{5}{34}m\right) for m.

$$m=\frac{845}{67}$$

Substitute \frac{845}{67} for m in the equation y=\frac{127}{34}-\frac{5}{34}m.

$$y=\frac{127}{34}-\frac{5}{34}\times \frac{845}{67}$$

Calculate y from y=\frac{127}{34}-\frac{5}{34}\times \frac{845}{67}.

$$y=\frac{126}{67}$$

Substitute \frac{126}{67} for y in the equation x=20-6y.

$$x=20-6\times \frac{126}{67}$$

Calculate x from x=20-6\times \frac{126}{67}.

$$x=\frac{584}{67}$$

The system is now solved.

$$x=\frac{584}{67} y=\frac{126}{67} m=\frac{845}{67}$$