Question

X + Y = 2. y=2x+5write the solution as an ordered pair

Answer 1

Given the following system of equations:

`\begin{cases}x+y=2 \\ y=2x+5\end{cases}`

notice that we can substitute the second equation on the first one to get the following:

`\begin{gathered} x+(2x+5)=2 \\ \Rightarrow x+2x=2-5 \\ \Rightarrow3x=-3 \\ \Rightarrow x=(-3)/(3)=-1 \\ x=-1 \end{gathered}`

now that we have that x = -1, we can use this value on the first equation to find the value of y:

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

therefore, the solution of the system is (-1,3)