Solve {l}{p/4-p-3/6=1}{q=p}{r=q}{s=r}{text{Solvefor}ttext{where}}{t=s}

$$\left. \begin{array} { l } { \frac{p}{4} - \frac{p - 3}{6} = 1 }\\ { q = p }\\ { r = q }\\ { s = r }\\ { \text{Solve for } t \text{ where} } \\ { t = s } \end{array} \right.$$

Solve for p, q, r, s, t

$$t=6$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 12, the least common multiple of 4,6.

$$3p-2\left(p-3\right)=12$$

Use the distributive property to multiply -2 by p-3.

$$3p-2p+6=12$$

Combine 3p and -2p to get p.

$$p+6=12$$

Subtract 6 from both sides.

$$p=12-6$$

Subtract 6 from 12 to get 6.

$$p=6$$

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

$$q=6$$

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

$$r=6$$

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

$$s=6$$

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

$$t=6$$

The system is now solved.

$$p=6 q=6 r=6 s=6 t=6$$