Question

Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or aninfinite number of solutions. If the system has one solution, find the solution.-1.1x + 0.1y = - 12.1-3.3x + 0.3y = -36.3

Answer 1

Adding 1.1x to the first equation we get:

$\begin{gathered} -1.1x+0.1y+1.1x=-12.1+1.1x, \\ 0.1y=-12.1+1.1x\text{.} \end{gathered}$

Multiplying the above equation by 10 we get:

$\begin{gathered} 0.1y\times10=-12.1\times10+1.1x\times10, \\ y=-121+11x\text{.} \end{gathered}$

Substituting the above equation in the second one we get:

$-3.3x+0.3(-121+11x)=-36.3.$

Simplifying the above equation we get:

$\begin{gathered} -3.3x-36.3+3.3x=-36.3, \\ -36.3=-36.3. \end{gathered}$

The last equation is true for all (x,y) therefore the system has infinitely many solutions.

Answer: Infinite Number of Solutions.