Q2. - Algebra 2

Question

2.FIND THE ERROR Melissa is solving the system of equations

$r+2s+t=3,2r+4s+2t-6,$ and$3r+6s+3t=12.$ Is she correct? Explain your reasoning.

Step-by-Step Solution

Answer

 Melissa is correct than the system of equation as infinitely many solutions, for the equation$r+2s+t=2$.

Step-1 –Condition for unique solution

Solution of a system of equation is unique, when number of equation =number of variable. 

Step-2 –Condition for infinite solution

The solution of system of equation has infinite solution when number of equation number of variables

Step-3 –Conclusion

Here, we see that two equations are the same plane so the solution has infinitely many solutions.

Step-4 –Concept of no solution

But if we consider the two equations

$r+2s+t=2$ and $3r+6s+3t=12$ ,then no solution is obtained because,$\begin{array}{c}3r+6s+3t=12\\ 3(r+2s+t)=12\\ 3\left(2\right)=126=12\end{array}$

Which is not possible.

Hence, if we take the first two equation then the solution has infinitely many solution but if we take the third equation then no solution is obtained.