Question

Solve the following system of equations.{x=2y−3 x−y=1Write your answer as an ordered pair in the form (x,y).

Answer 1

Solve the system of equations:

`\begin{gathered} x=2y-3\ldots\ldots\ldots\text{.}(1) \\ x-y=1\ldots\ldots\ldots\text{.}(2) \end{gathered}`

step 1: Substitute the value of 2y-3 for x in equation (2) and solve for y

`\begin{gathered} x-y=1\ldots\ldots\ldots\text{.}(2) \\ (2y-3)-y=1 \\ 2y-3-y=1 \\ \text{ collect like terms} \\ 2y-y=1+3 \\ y=4 \end{gathered}`

step 2: Solve for x by substituting 4 for y in equation (1)

`\begin{gathered} x=2y-3\ldots\ldots\ldots\text{.}(1) \\ \text{put }y=4 \\ x=2(4)-3 \\ x=8-3 \\ x=5 \end{gathered}`

Therefore, the solution to the system of equations in ordered pair is

`(x,y)=(5,4)`