Solve {l}{f=1/2x+1}{y=2/5x-1}

$$\left. \begin{array} { l } { f = \frac { 1 } { 2 } x + 1 } \\ { y = \frac { 2 } { 5 } x - 1 } \end{array} \right.$$

Solve for x, y

$$x=2f-2$$

$$y=\frac{4f-9}{5}$$

Steps Using Substitution

Consider the first equation. Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}x+1=f$$

Subtract 1 from both sides.

$$\frac{1}{2}x=f-1$$

Consider the second equation. Subtract \frac{2}{5}x from both sides.

$$y-\frac{2}{5}x=-1$$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$\frac{1}{2}x=f-1,-\frac{2}{5}x+y=-1$$

Pick one of the two equations which is more simple to solve for x by isolating x on the left hand side of the equal sign.

$$\frac{1}{2}x=f-1$$

Multiply both sides by 2.

$$x=2f-2$$

Substitute 2f-2 for x in the other equation, -\frac{2}{5}x+y=-1.

$$-\frac{2}{5}\left(2f-2\right)+y=-1$$

Multiply -\frac{2}{5} times -2+2f.

$$\frac{4-4f}{5}+y=-1$$

Subtract \frac{4-4f}{5} from both sides of the equation.

$$y=\frac{4f-9}{5}$$

The system is now solved.

$$x=2f-2,y=\frac{4f-9}{5}$$