Solve {l}{2=-a+b}{1=a}{-3=-2a-2b+c}

$$\left. \begin{array} { l } { 2 = - a + b } \\ { 1 = a } \\ { - 3 = - 2 a - 2 b + c } \end{array} \right.$$

Solve for a, b, c

$$a=1$$

$$b=3$$

$$c=5$$

Solution Steps

Consider the second equation. Swap sides so that all variable terms are on the left hand side.

$$a=1$$

Consider the first equation. Insert the known values of variables into the equation.

$$2=-1+b$$

Swap sides so that all variable terms are on the left hand side.

$$-1+b=2$$

Add 1 to both sides.

$$b=2+1$$

Add 2 and 1 to get 3.

$$b=3$$

Consider the third equation. Insert the known values of variables into the equation.

$$-3=-2-2\times 3+c$$

Do the multiplications.

$$-3=-2-6+c$$

Subtract 6 from -2 to get -8.

$$-3=-8+c$$

Swap sides so that all variable terms are on the left hand side.

$$-8+c=-3$$

Add 8 to both sides.

$$c=-3+8$$

Add -3 and 8 to get 5.

$$c=5$$

The system is now solved.

$$a=1 b=3 c=5$$