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

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

Solve for p, q, r

$$r=6$$

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.

$$r=6$$

The system is now solved.

$$p=6 q=6 r=6$$