Question

Use substitution to solve the system of equations. How many solutions are there?1/2x-1/3y=5X=2/3y+10A. There are no solutionsB. There is one solutionC. There are intinitely many solutionsD. It is not possible to determine the number of solutions

Answer 1

In order to solve the system using substitution, we can use the value of x from the second equation in the first one. So we have:

`\begin{gathered} (1)/(2)x-(1)/(3)y=5 \\ (1)/(2)((2)/(3)y+10)-(1)/(3)y=5 \\ (1)/(3)y+5-(1)/(3)y=5 \\ 5=5 \end{gathered}`

Since the final sentence is true, we have an infinite number of solutions for this system, therefore the correct option is C.