Solve {l}{1/3a-4+9=7}{5b+6-6b+2=19}

$$\left. \begin{array} { l } { \frac { 1 } { 3 } a - 4 + 9 = 7 } \\ { 5 b + 6 - 6 b + 2 = 19 } \end{array} \right.$$

Solve for a, b

$$a=6$$

$$b=-11$$

Solution Steps

Consider the first equation. Add -4 and 9 to get 5.

$$\frac{1}{3}a+5=7$$

Subtract 5 from both sides.

$$\frac{1}{3}a=7-5$$

Subtract 5 from 7 to get 2.

$$\frac{1}{3}a=2$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$a=2\times 3$$

Multiply 2 and 3 to get 6.

$$a=6$$

Consider the second equation. Combine 5b and -6b to get -b.

$$-b+6+2=19$$

Add 6 and 2 to get 8.

$$-b+8=19$$

Subtract 8 from both sides.

$$-b=19-8$$

Subtract 8 from 19 to get 11.

$$-b=11$$

Divide both sides by -1.

$$b=-11$$

The system is now solved.

$$a=6 b=-11$$