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

What Is The Nature Of The Solution Set To The Following System Of Equationsx Y 32x 5y 12 class=

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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

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