Solve {l}{r-6/2=r+3/4}{s=7r+6}{text{Solvefor}ttext{where}}{t=s}

$$\left. \begin{array} { l } { \frac{r - 6}{2} = \frac{r + 3}{4} }\\ { s = 7 r + 6 }\\ { \text{Solve for } t \text{ where} } \\ { t = s } \end{array} \right.$$

Solve for r, s, t

$$t=111$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(r-6\right)=r+3$$

Use the distributive property to multiply 2 by r-6.

$$2r-12=r+3$$

Subtract r from both sides.

$$2r-12-r=3$$

Combine 2r and -r to get r.

$$r-12=3$$

Add 12 to both sides.

$$r=3+12$$

Add 3 and 12 to get 15.

$$r=15$$

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

$$s=7\times 15+6$$

Multiply 7 and 15 to get 105.

$$s=105+6$$

Add 105 and 6 to get 111.

$$s=111$$

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

$$t=111$$

The system is now solved.

$$r=15 s=111 t=111$$