Question

What is the nature of the solution set to the following system of equations?x + y = 32x + 5y = 12

Answer 1

SOLUTIONS

What is the nature of the solution set to the following system of equations?

`\begin{gathered} x+y=3 \\ 2x+5y=12 \end{gathered}`

Using a substitution method:

`\begin{gathered} x+y=3 \\ x=3-y \end{gathered}`

sub the x value to equation 1

`\begin{gathered} 2x+5y=12 \\ 2(3-y)+5y=12 \\ 6-2y+5y=12 \\ 3y=12-6 \\ 3y=6 \\ y=(6)/(3) \\ y=2 \end{gathered}`

since the value of y = 2, solve for x

`\begin{gathered} x+y=3 \\ x+2=3 \\ x=3-2 \\ x=1 \end{gathered}`

Therefore the solution is 1 , 2

Answer = Option B