Solve {l}{x+y=7}{x+y+45=10y+x}

$$\left\{ \begin{array} { l } { x + y = 7 } \\ { x + y + 45 = 10 y + x } \end{array} \right.$$

Solve for x, y

$$x=2$$

$$y=5$$

Solution Steps

Consider the second equation. Subtract 10y from both sides.

$$x+y+45-10y=x$$

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

$$x-9y+45=x$$

Subtract x from both sides.

$$x-9y+45-x=0$$

Combine x and -x to get 0.

$$-9y+45=0$$

Subtract 45 from both sides. Anything subtracted from zero gives its negation.

$$-9y=-45$$

Divide both sides by -9.

$$y=\frac{-45}{-9}$$

Divide -45 by -9 to get 5.

$$y=5$$

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

$$x+5=7$$

Subtract 5 from both sides.

$$x=7-5$$

Subtract 5 from 7 to get 2.

$$x=2$$

The system is now solved.

$$x=2 y=5$$