Solve {l}{x+y=4}{(x+y)-(10y+x)=27}

$$\left\{ \begin{array} { l } { x + y = 4 } \\ { ( x + y ) - ( 10 y + x ) = 27 } \end{array} \right.$$

Solve for x, y

$$x=7$$

$$y=-3$$

Solution Steps

Consider the second equation. To find the opposite of 10y+x, find the opposite of each term.

$$x+y-10y-x=27$$

Combine y and -10y to get -9y.

$$x-9y-x=27$$

Combine x and -x to get 0.

$$-9y=27$$

Divide both sides by -9.

$$y=\frac{27}{-9}$$

Divide 27 by -9 to get -3.

$$y=-3$$

Consider the first equation. Insert the known values of variables into the equation.

$$x-3=4$$

Add 3 to both sides.

$$x=4+3$$

Add 4 and 3 to get 7.

$$x=7$$

The system is now solved.

$$x=7 y=-3$$