Solve {l}{3a+5b-2-c=0}{2a+3b-c=0}{a+b=199}

$$\left\{ \begin{array} { l } { 3 a + 5 b - 2 - c = 0 } \\ { 2 a + 3 b - c = 0 } \\ { a + b = 199 } \end{array} \right.$$

Solve for a, b, c

$$a=396$$

$$b=-197$$

$$c=201$$

Short Steps Using Substitution

Solve 3a+5b-2-c=0 for c.

$$c=3a+5b-2$$

Substitute 3a+5b-2 for c in the equation 2a+3b-c=0.

$$2a+3b-\left(3a+5b-2\right)=0$$

Solve the second equation for b and the third equation for a.

$$b=-\frac{1}{2}a+1 a=-b+199$$

Substitute -\frac{1}{2}a+1 for b in the equation a=-b+199.

$$a=-\left(-\frac{1}{2}a+1\right)+199$$

Solve a=-\left(-\frac{1}{2}a+1\right)+199 for a.

$$a=396$$

Substitute 396 for a in the equation b=-\frac{1}{2}a+1.

$$b=-\frac{1}{2}\times 396+1$$

Calculate b from b=-\frac{1}{2}\times 396+1.

$$b=-197$$

Substitute -197 for b and 396 for a in the equation c=3a+5b-2.

$$c=3\times 396+5\left(-197\right)-2$$

Calculate c from c=3\times 396+5\left(-197\right)-2.

$$c=201$$

The system is now solved.

$$a=396 b=-197 c=201$$