Solve {l}{A=9-4+(6-11)-(-8+3-2)}{B=-16-(7-15+4)-(-5+12)}{C=7-5+(2-3)-(-7+5-3)}

$$\left. \begin{array} { l } { A = 9 - 4 + ( 6 - 11 ) - ( - 8 + 3 - 2 ) } \\ { B = - 16 - ( 7 - 15 + 4 ) - ( - 5 + 12 ) } \\ { C = 7 - 5 + ( 2 - 3 ) - ( - 7 + 5 - 3 ) } \end{array} \right.$$

Solve for A, B, C

$$A=7$$

$$B=-19$$

$$C=6$$

Solution Steps

Consider the first equation. Subtract 4 from 9 to get 5.

$$A=5+6-11-\left(-8+3-2\right)$$

Add 5 and 6 to get 11.

$$A=11-11-\left(-8+3-2\right)$$

Subtract 11 from 11 to get 0.

$$A=0-\left(-8+3-2\right)$$

Add -8 and 3 to get -5.

$$A=0-\left(-5-2\right)$$

Subtract 2 from -5 to get -7.

$$A=0-\left(-7\right)$$

The opposite of -7 is 7.

$$A=0+7$$

Add 0 and 7 to get 7.

$$A=7$$

Consider the second equation. Subtract 15 from 7 to get -8.

$$B=-16-\left(-8+4\right)-\left(-5+12\right)$$

Add -8 and 4 to get -4.

$$B=-16-\left(-4\right)-\left(-5+12\right)$$

The opposite of -4 is 4.

$$B=-16+4-\left(-5+12\right)$$

Add -16 and 4 to get -12.

$$B=-12-\left(-5+12\right)$$

Add -5 and 12 to get 7.

$$B=-12-7$$

Subtract 7 from -12 to get -19.

$$B=-19$$

Consider the third equation. Subtract 5 from 7 to get 2.

$$C=2+2-3-\left(-7+5-3\right)$$

Add 2 and 2 to get 4.

$$C=4-3-\left(-7+5-3\right)$$

Subtract 3 from 4 to get 1.

$$C=1-\left(-7+5-3\right)$$

Add -7 and 5 to get -2.

$$C=1-\left(-2-3\right)$$

Subtract 3 from -2 to get -5.

$$C=1-\left(-5\right)$$

The opposite of -5 is 5.

$$C=1+5$$

Add 1 and 5 to get 6.

$$C=6$$

The system is now solved.

$$A=7 B=-19 C=6$$