Solve {l}{2y+x+y=16}{200+10x+y-227=100y+10x+2y}

$$\left\{ \begin{array} { l } { 2 y + x + y = 16 } \\ { 200 + 10 x + y - 227 = 100 y + 10 x + 2 y } \end{array} \right.$$

Solve for y, x

$$x = \frac{1697}{101} = 16\frac{81}{101} \approx 16.801980198$$

$$y=-\frac{27}{101}\approx -0.267326733$$

Solution Steps

Consider the first equation. Combine 2y and y to get 3y.

$$3y+x=16$$

Consider the second equation. Subtract 227 from 200 to get -27.

$$-27+10x+y=100y+10x+2y$$

Combine 100y and 2y to get 102y.

$$-27+10x+y=102y+10x$$

Subtract 102y from both sides.

$$-27+10x+y-102y=10x$$

Combine y and -102y to get -101y.

$$-27+10x-101y=10x$$

Subtract 10x from both sides.

$$-27+10x-101y-10x=0$$

Combine 10x and -10x to get 0.

$$-27-101y=0$$

Add 27 to both sides. Anything plus zero gives itself.

$$-101y=27$$

Divide both sides by -101.

$$y=-\frac{27}{101}$$

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

$$3\left(-\frac{27}{101}\right)+x=16$$

Multiply 3 and -\frac{27}{101} to get -\frac{81}{101}.

$$-\frac{81}{101}+x=16$$

Add \frac{81}{101} to both sides.

$$x=16+\frac{81}{101}$$

Add 16 and \frac{81}{101} to get \frac{1697}{101}.

$$x=\frac{1697}{101}$$

The system is now solved.

$$y=-\frac{27}{101} x=\frac{1697}{101}$$