Solve {l}{25+5y+t=0}{5+x-2y+t=0}{25-3x-4y+t=0}

$$\left\{ \begin{array} { l } { 25 + 5 y + t = 0 } \\ { 5 + x - 2 y + t = 0 } \\ { 25 - 3 x - 4 y + t = 0 } \end{array} \right.$$

Solve for y, t, x

$$x=6$$

$$y=-2$$

$$t=-15$$

Short Steps Using Substitution

Solve 25+5y+t=0 for t.

$$t=-25-5y$$

Substitute -25-5y for t in the second and third equation.

$$5+x-2y-25-5y=0 25-3x-4y-25-5y=0$$

Solve these equations for y and x respectively.

$$y=-\frac{20}{7}+\frac{1}{7}x x=-3y$$

Substitute -\frac{20}{7}+\frac{1}{7}x for y in the equation x=-3y.

$$x=-3\left(-\frac{20}{7}+\frac{1}{7}x\right)$$

Solve x=-3\left(-\frac{20}{7}+\frac{1}{7}x\right) for x.

$$x=6$$

Substitute 6 for x in the equation y=-\frac{20}{7}+\frac{1}{7}x.

$$y=-\frac{20}{7}+\frac{1}{7}\times 6$$

Calculate y from y=-\frac{20}{7}+\frac{1}{7}\times 6.

$$y=-2$$

Substitute -2 for y in the equation t=-25-5y.

$$t=-25-5\left(-2\right)$$

Calculate t from t=-25-5\left(-2\right).

$$t=-15$$

The system is now solved.

$$y=-2 t=-15 x=6$$