Solve {l}{4a+2b+c=4}{4a-2b+c=-2}{4a+b=0,5}

$$\left\{ \begin{array} { l } { 4 a + 2 b + c = 4 } \\ { 4 a - 2 b + c = - 2 } \\ { 4 a + b = 0,5 } \end{array} \right.$$

Solve for a, b, c

$$a=-0,25$$

$$b=1,5$$

$$c=2$$

Short Steps Using Substitution

Solve 4a+2b+c=4 for c.

$$c=4-4a-2b$$

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

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

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

$$b=\frac{3}{2} a=-\frac{1}{4}b+\frac{1}{8}$$

Substitute \frac{3}{2} for b in the equation a=-\frac{1}{4}b+\frac{1}{8}.

$$a=-\frac{1}{4}\times \frac{3}{2}+\frac{1}{8}$$

Calculate a from a=-\frac{1}{4}\times \frac{3}{2}+\frac{1}{8}.

$$a=-\frac{1}{4}$$

Substitute \frac{3}{2} for b and -\frac{1}{4} for a in the equation c=4-4a-2b.

$$c=4-4\left(-\frac{1}{4}\right)-2\times \frac{3}{2}$$

Calculate c from c=4-4\left(-\frac{1}{4}\right)-2\times \frac{3}{2}.

$$c=2$$

The system is now solved.

$$a=-\frac{1}{4} b=\frac{3}{2} c=2$$