Solve {l}{4x+3y-9=0}{3x-2y-11=0}{5x+6y+k=0}

$$\left. \begin{array} { l } { 4 x + 3 y - 9 = 0 } \\ { 3 x - 2 y - 11 = 0 } \\ { 5 x + 6 y + k = 0 } \end{array} \right.$$

Solve for x, y, k

$$x=3$$

$$y=-1$$

$$k=-9$$

Short Steps Using Substitution

Solve 4x+3y-9=0 for x.

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

Substitute \frac{9}{4}-\frac{3}{4}y for x in the second and third equation.

$$3\left(\frac{9}{4}-\frac{3}{4}y\right)-2y-11=0 5\left(\frac{9}{4}-\frac{3}{4}y\right)+6y+k=0$$

Solve these equations for y and k respectively.

$$y=-1 k=-\frac{45}{4}-\frac{9}{4}y$$

Substitute -1 for y in the equation k=-\frac{45}{4}-\frac{9}{4}y.

$$k=-\frac{45}{4}-\frac{9}{4}\left(-1\right)$$

Calculate k from k=-\frac{45}{4}-\frac{9}{4}\left(-1\right).

$$k=-9$$

Substitute -1 for y in the equation x=\frac{9}{4}-\frac{3}{4}y.

$$x=\frac{9}{4}-\frac{3}{4}\left(-1\right)$$

Calculate x from x=\frac{9}{4}-\frac{3}{4}\left(-1\right).

$$x=3$$

The system is now solved.

$$x=3 y=-1 k=-9$$