Solve {c}{64-4x-4y+lambda=0}{-4x-8y+32+lambda=0}{x+y-50=0}

$$\left. \begin{array} { c } { 64 - 4 x - 4 y + \lambda = 0 } \\ { - 4 x - 8 y + 32 + \lambda = 0 } \\ { x + y - 50 = 0 } \end{array} \right.$$

Solve for x, y, λ

$$x=58$$

$$y=-8$$

$$\lambda =136$$

Short Steps Using Substitution

Solve 64-4x-4y+\lambda =0 for \lambda .

$$\lambda =-64+4x+4y$$

Substitute -64+4x+4y for \lambda in the equation -4x-8y+32+\lambda =0.

$$-4x-8y+32-64+4x+4y=0$$

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

$$y=-8 x=-y+50$$

Substitute -8 for y in the equation x=-y+50.

$$x=-\left(-8\right)+50$$

Calculate x from x=-\left(-8\right)+50.

$$x=58$$

Substitute -8 for y and 58 for x in the equation \lambda =-64+4x+4y.

$$\lambda =-64+4\times 58+4\left(-8\right)$$

Calculate \lambda from \lambda =-64+4\times 58+4\left(-8\right).

$$\lambda =136$$

The system is now solved.

$$x=58 y=-8 \lambda =136$$