Solve {c}{D-G=0}{-A+2D-G=1}{A-D+2G=0}

$$\left\{ \begin{array} { c } { D - G = 0 } \\ { - A + 2 D - G = 1 } \\ { A - D + 2 G = 0 } \end{array} \right.$$

Solve for D, G, A

$$D=\frac{1}{2}=0.5$$

$$G=\frac{1}{2}=0.5$$

$$A=-\frac{1}{2}=-0.5$$

Short Steps Using Substitution

Solve D-G=0 for D.

$$D=G$$

Substitute G for D in the second and third equation.

$$-A+2G-G=1 A-G+2G=0$$

Solve these equations for G and A respectively.

$$G=A+1 A=-G$$

Substitute A+1 for G in the equation A=-G.

$$A=-\left(A+1\right)$$

Solve A=-\left(A+1\right) for A.

$$A=-\frac{1}{2}$$

Substitute -\frac{1}{2} for A in the equation G=A+1.

$$G=-\frac{1}{2}+1$$

Calculate G from G=-\frac{1}{2}+1.

$$G=\frac{1}{2}$$

Substitute \frac{1}{2} for G in the equation D=G.

$$D=\frac{1}{2}$$

The system is now solved.

$$D=\frac{1}{2} G=\frac{1}{2} A=-\frac{1}{2}$$