System solved by substitution

Problem

A kinematics problem leads to the following system, in which $b=1$ and $B=5$ are known. Simplify the system by substituting the known values: $\begin{cases} b = 1,\; B = 5 \\ a = \frac{8}{5}P \\ \mu = P \\ A+P+B = 2A \\ A+P+B = a+\mu+b \end{cases}$

Solution

Substitute the known values $b=1$ and $B=5$ into the equations that contain them; the first two relations remain unchanged: $\begin{cases} a = \frac{8}{5}P \\ \mu = P \\ A+P+5 = 2A \\ A+P+5 = a+\mu+1 \end{cases}$ The system is now ready for the subsequent substitutions: from the third equation we obtain $A = P+5$, which can be inserted into the last one together with $a=\tfrac{8}{5}P$ and $\mu=P$.

Links

Topics: Linear systems
Concepts: Substitution method · System of equations
Methods: Systems substitution
Skills: Solve systems
Exercise type: System solving