Solve {l}{y=x-p/2}{y=2p}

$$\left\{ \begin{array} { l } { y = x - \frac { p } { 2 } } \\ { y = 2 p } \end{array} \right.$$

Solve for x, y

$$x=\frac{5p}{2}$$

$$y=2p$$

Steps Using Substitution

Consider the first equation. Subtract x from both sides.

$$y-x=-\frac{p}{2}$$

Multiply both sides of the equation by 2.

$$2y-2x=-p$$

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.

$$y=2p,2y-2x=-p$$

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

$$y=2p$$

Substitute 2p for y in the other equation, 2y-2x=-p.

$$2\times 2p-2x=-p$$

Multiply 2 times 2p.

$$4p-2x=-p$$

Subtract 4p from both sides of the equation.

$$-2x=-5p$$

Divide both sides by -2.

$$x=\frac{5p}{2}$$

The system is now solved.

$$y=2p,x=\frac{5p}{2}$$