Solve {l}{1/2varphi=1/4x}{1/4x=5}

$$\left. \begin{array} { l } { \frac { 1 } { 2 } \varphi = \frac { 1 } { 4 } x } \\ { \frac { 1 } { 4 } x = 5 } \end{array} \right.$$

Solve for φ, x

$$x=20$$

$$\phi =10$$

Solution Steps

Consider the second equation. Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x=5\times 4$$

Multiply 5 and 4 to get 20.

$$x=20$$

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

$$\frac{1}{2}\phi =\frac{1}{4}\times 20$$

Multiply \frac{1}{4} and 20 to get 5.

$$\frac{1}{2}\phi =5$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$\phi =5\times 2$$

Multiply 5 and 2 to get 10.

$$\phi =10$$

The system is now solved.

$$\phi =10 x=20$$