Solve {r}{3r+4/7p=8}{-r-3/5r=1/3}

$$\left. \begin{array} { r } { 3 r + \frac { 4 } { 7 } p = 8 } \\ { - r - \frac { 3 } { 5 } r = \frac { 1 } { 3 } } \end{array} \right.$$

Solve for r, p

$$r=-\frac{5}{24}\approx -0.208333333$$

$$p = \frac{483}{32} = 15\frac{3}{32} = 15.09375$$

Solution Steps

Consider the second equation. Combine -r and -\frac{3}{5}r to get -\frac{8}{5}r.

$$-\frac{8}{5}r=\frac{1}{3}$$

Multiply both sides by -\frac{5}{8}, the reciprocal of -\frac{8}{5}.

$$r=\frac{1}{3}\left(-\frac{5}{8}\right)$$

Multiply \frac{1}{3} and -\frac{5}{8} to get -\frac{5}{24}.

$$r=-\frac{5}{24}$$

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

$$3\left(-\frac{5}{24}\right)+\frac{4}{7}p=8$$

Multiply 3 and -\frac{5}{24} to get -\frac{5}{8}.

$$-\frac{5}{8}+\frac{4}{7}p=8$$

Add \frac{5}{8} to both sides.

$$\frac{4}{7}p=8+\frac{5}{8}$$

Add 8 and \frac{5}{8} to get \frac{69}{8}.

$$\frac{4}{7}p=\frac{69}{8}$$

Multiply both sides by \frac{7}{4}, the reciprocal of \frac{4}{7}.

$$p=\frac{69}{8}\times \frac{7}{4}$$

Multiply \frac{69}{8} and \frac{7}{4} to get \frac{483}{32}.

$$p=\frac{483}{32}$$

The system is now solved.

$$r=-\frac{5}{24} p=\frac{483}{32}$$