Solve {c}{(10x+y)+y+x=91}{91-x+y=(10x+y)}

$$\left. \begin{array} { c } { ( 10 x + y ) + y + x = 91 } \\ { 91 - x + y = ( 10 x + y ) } \end{array} \right.$$

Solve for x, y

$$x = \frac{91}{11} = 8\frac{3}{11} \approx 8.272727273$$

$$y=0$$

Solution Steps

Consider the first equation. Combine y and y to get 2y.

$$10x+2y+x=91$$

Combine 10x and x to get 11x.

$$11x+2y=91$$

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

$$91-x+y-10x=y$$

Combine -x and -10x to get -11x.

$$91-11x+y=y$$

Subtract y from both sides.

$$91-11x+y-y=0$$

Combine y and -y to get 0.

$$91-11x=0$$

Subtract 91 from both sides. Anything subtracted from zero gives its negation.

$$-11x=-91$$

Divide both sides by -11.

$$x=\frac{-91}{-11}$$

Fraction \frac{-91}{-11} can be simplified to \frac{91}{11} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{91}{11}$$

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

$$11\times \frac{91}{11}+2y=91$$

Multiply 11 and \frac{91}{11} to get 91.

$$91+2y=91$$

Subtract 91 from both sides.

$$2y=91-91$$

Subtract 91 from 91 to get 0.

$$2y=0$$

Divide both sides by 2. Zero divided by any non-zero number gives zero.

$$y=0$$

The system is now solved.

$$x=\frac{91}{11} y=0$$