Solve {l}{4a+7b=-9}{8a+2c=-24}{6b+2c=14}

$$\left. \begin{array} { l } { 4 a + 7 b = - 9 } \\ { 8 a + 2 c = - 24 } \\ { 6 b + 2 c = 14 } \end{array} \right.$$

Solve for a, b, c

$$a=-4$$

$$b=1$$

$$c=4$$

Short Steps Using Substitution

Solve 4a+7b=-9 for a.

$$a=-\frac{7}{4}b-\frac{9}{4}$$

Substitute -\frac{7}{4}b-\frac{9}{4} for a in the equation 8a+2c=-24.

$$8\left(-\frac{7}{4}b-\frac{9}{4}\right)+2c=-24$$

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

$$b=\frac{3}{7}+\frac{1}{7}c c=7-3b$$

Substitute \frac{3}{7}+\frac{1}{7}c for b in the equation c=7-3b.

$$c=7-3\left(\frac{3}{7}+\frac{1}{7}c\right)$$

Solve c=7-3\left(\frac{3}{7}+\frac{1}{7}c\right) for c.

$$c=4$$

Substitute 4 for c in the equation b=\frac{3}{7}+\frac{1}{7}c.

$$b=\frac{3}{7}+\frac{1}{7}\times 4$$

Calculate b from b=\frac{3}{7}+\frac{1}{7}\times 4.

$$b=1$$

Substitute 1 for b in the equation a=-\frac{7}{4}b-\frac{9}{4}.

$$a=-\frac{7}{4}-\frac{9}{4}$$

Calculate a from a=-\frac{7}{4}-\frac{9}{4}.

$$a=-4$$

The system is now solved.

$$a=-4 b=1 c=4$$