Solve {l}{-4=9a-3b+c}{-4=4a+2a+c}{-10=9a+3a+c}

$$\left. \begin{array} { l } { - 4 = 9 a - 3 b + c } \\ { - 4 = 4 a + 2 a + c } \\ { - 10 = 9 a + 3 a + c } \end{array} \right.$$

Solve for a, b, c

$$a=-1$$

$$b=-1$$

$$c=2$$

Short Steps Using Substitution

Solve -4=9a-3b+c for c.

$$c=-9a-4+3b$$

Substitute -9a-4+3b for c in the second and third equation.

$$-4=4a+2a-9a-4+3b -10=9a+3a-9a-4+3b$$

Solve these equations for b and a respectively.

$$b=a a=-2-b$$

Substitute a for b in the equation a=-2-b.

$$a=-2-a$$

Solve a=-2-a for a.

$$a=-1$$

Substitute -1 for a in the equation b=a.

$$b=-1$$

Substitute -1 for b and -1 for a in the equation c=-9a-4+3b.

$$c=-9\left(-1\right)-4+3\left(-1\right)$$

Calculate c from c=-9\left(-1\right)-4+3\left(-1\right).

$$c=2$$

The system is now solved.

$$a=-1 b=-1 c=2$$