Question

Consider the following system of equations 2x+y=8 x-2y=-1Determine the solution to the system of equations

Answer 1

Given

`2x+y=8,x-2y=-1`

Find

Solution to the system of equations

Step-by-step explanation

To find the solution we can use various methods . but here we will use substitution method.

2x+y=8 , from this equation we find the value of y and then substitute it in other equation.

`\begin{gathered} 2x+y=8 \\ y=8-2x.................................(1) \end{gathered}`

now, put it in second equation

`\begin{gathered} x-2y=-1 \\ x-2(8-2x)=-1 \\ x-16+4x=-1 \\ 5x=15 \\ x=3 \end{gathered}`

put value of x in 1 to find y.

`\begin{gathered} y=8-2x \\ y=8-6 \\ y=2 \end{gathered}`

Final Answer

Solution to the equations is x = 3 and y = 2