Question

Find the solution to the system of equations 2x + y = 3 and x - y = 3.(-2, 1)(-2, -1)(2, -1)(2, 1)

Answer 1

Use the elimination method to solve the system of equations:

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

Add both equations to eliminate the variable y. This can be done because the coefficient of y in the first equation is 1, while the coefficient of y in the second equation is -1:

$\begin{gathered} (2x+y)+(x-y)=(3)+(3) \\ \\ \Rightarrow2x+y+x-y=3+3 \\ \\ \Rightarrow2x+x+y-y=6 \\ \\ \Rightarrow3x+0=6 \\ \\ \Rightarrow3x=6 \\ \\ \Rightarrow x=\frac{6}{3} \\ \\ \therefore x=2 \end{gathered}$

Replace x=2 into the first equation and solve for y:

$\begin{gathered} 2x+y=3 \\ \\ \Rightarrow2(2)+y=3 \\ \\ \Rightarrow4+y=3 \\ \\ \Rightarrow y=3-4 \\ \\ \therefore y=-1 \end{gathered}$

Then, the solution to the system is x=2 and y=-1. Using the ordered pair notation (x,y), the solution to the system is (2,-1).

Therefore, the correct choice is:

$(2,-1)$