Solve {l}{x-3y=5}{x-2y=k}{k=0.5y+2.5}

$$\left\{ \begin{array} { l } { x - 3 y = 5 } \\ { x - 2 y = k } \\ { k = 0.5 y + 2.5 } \end{array} \right.$$

Solve for x, y, k

$$x=-10$$

$$y=-5$$

$$k=0$$

Short Steps Using Substitution

Reorder the equations.

$$x-2y=k x-3y=5 k=0.5y+2.5$$

Solve x-2y=k for k.

$$k=x-2y$$

Substitute x-2y for k in the equation k=0.5y+2.5.

$$x-2y=0.5y+2.5$$

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

$$y=-\frac{5}{3}+\frac{1}{3}x x=2.5+2.5y$$

Substitute -\frac{5}{3}+\frac{1}{3}x for y in the equation x=2.5+2.5y.

$$x=2.5+2.5\left(-\frac{5}{3}+\frac{1}{3}x\right)$$

Solve x=2.5+2.5\left(-\frac{5}{3}+\frac{1}{3}x\right) for x.

$$x=-10$$

Substitute -10 for x in the equation y=-\frac{5}{3}+\frac{1}{3}x.

$$y=-\frac{5}{3}+\frac{1}{3}\left(-10\right)$$

Calculate y from y=-\frac{5}{3}+\frac{1}{3}\left(-10\right).

$$y=-5$$

Substitute -5 for y and -10 for x in the equation k=x-2y.

$$k=-10-2\left(-5\right)$$

Calculate k from k=-10-2\left(-5\right).

$$k=0$$

The system is now solved.

$$x=-10 y=-5 k=0$$