SOLUTIONS
What is the nature of the solution set to the following system of equations?
[tex]\begin{gathered} x+y=3 \\ 2x+5y=12 \end{gathered}[/tex]
Using a substitution method:
[tex]\begin{gathered} x+y=3 \\ x=3-y \end{gathered}[/tex]
sub the x value to equation 1
[tex]\begin{gathered} 2x+5y=12 \\ 2(3-y)+5y=12 \\ 6-2y+5y=12 \\ 3y=12-6 \\ 3y=6 \\ y=\frac{6}{3} \\ y=2 \end{gathered}[/tex]
since the value of y = 2, solve for x
[tex]\begin{gathered} x+y=3 \\ x+2=3 \\ x=3-2 \\ x=1 \end{gathered}[/tex]
Therefore the solution is 1 , 2
Answer = Option B
