Question

Solve the following system of equations. How many solutions are there? x + y = 2 5x + 5y = 10 a) There is no solution. b) There are infinite solutions. c) There is one solution.

Answer 1

we are given the following system of equations:

`\begin{gathered} x+y=2,\text{ (1)} \\ 5x+5y=10,\text{ (2)} \end{gathered}`

Equation (2) can be rewritten dividing by 5 on both sides as:

`(5x)/(5)+(5y)/(5)=(10)/(5)`

Solving the operations:

`x+y=2,\text{ (2)}`

Since equation (2) is the same equation as equation(1), this means that the system has infinite solutions.