Solve {l}{2b-c=1}{4a+c=-4}{2a+2b-4=2}

$$\left\{ \begin{array} { l } { 2 b - c = 1 } \\ { 4 a + c = - 4 } \\ { 2 a + 2 b - 4 = 2 } \end{array} \right.$$

Solve for b, c, a

$$b = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

$$c=14$$

$$a = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

Short Steps Using Substitution

Solve 2b-c=1 for c.

$$c=2b-1$$

Substitute 2b-1 for c in the equation 4a+c=-4.

$$4a+2b-1=-4$$

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

$$b=-2a-\frac{3}{2} a=3-b$$

Substitute -2a-\frac{3}{2} for b in the equation a=3-b.

$$a=3-\left(-2a-\frac{3}{2}\right)$$

Solve a=3-\left(-2a-\frac{3}{2}\right) for a.

$$a=-\frac{9}{2}$$

Substitute -\frac{9}{2} for a in the equation b=-2a-\frac{3}{2}.

$$b=-2\left(-\frac{9}{2}\right)-\frac{3}{2}$$

Calculate b from b=-2\left(-\frac{9}{2}\right)-\frac{3}{2}.

$$b=\frac{15}{2}$$

Substitute \frac{15}{2} for b in the equation c=2b-1.

$$c=2\times \frac{15}{2}-1$$

Calculate c from c=2\times \frac{15}{2}-1.

$$c=14$$

The system is now solved.

$$b=\frac{15}{2} c=14 a=-\frac{9}{2}$$