Solve {l}{209-((145+x)-12)+96=123}{18+(159-y)+34=172}

$$\left. \begin{array} { l } { 209 - ( ( 145 + x ) - 12 ) + 96 = 123 } \\ { 18 + ( 159 - y ) + 34 = 172 } \end{array} \right.$$

Solve for x, y

$$x=49$$

$$y=39$$

Solution Steps

Consider the first equation. Subtract 12 from 145 to get 133.

$$209-\left(133+x\right)+96=123$$

To find the opposite of 133+x, find the opposite of each term.

$$209-133-x+96=123$$

Subtract 133 from 209 to get 76.

$$76-x+96=123$$

Add 76 and 96 to get 172.

$$172-x=123$$

Subtract 172 from both sides.

$$-x=123-172$$

Subtract 172 from 123 to get -49.

$$-x=-49$$

Divide both sides by -1.

$$x=\frac{-49}{-1}$$

Fraction \frac{-49}{-1} can be simplified to 49 by removing the negative sign from both the numerator and the denominator.

$$x=49$$

Consider the second equation. Add 18 and 159 to get 177.

$$177-y+34=172$$

Add 177 and 34 to get 211.

$$211-y=172$$

Subtract 211 from both sides.

$$-y=172-211$$

Subtract 211 from 172 to get -39.

$$-y=-39$$

Divide both sides by -1.

$$y=\frac{-39}{-1}$$

Fraction \frac{-39}{-1} can be simplified to 39 by removing the negative sign from both the numerator and the denominator.

$$y=39$$

The system is now solved.

$$x=49 y=39$$