Question

Solutions to systems (3,1)Y = 2x - 52x-5y = 1

Answer 1

Given the equations:

`\begin{gathered} 1)y=2x-5 \\ 2)2x-5y=1 \end{gathered}`

To solve this equation system, you have to replace the first one into the second one:

`2x-5(2x-5)=1`

Solve the term in parentheses using the distributive propperty of multiplication

`\begin{gathered} 2x-5\cdot2x-5\cdot(-5)=1 \\ 2x-10x+10=1 \end{gathered}`

Solve for x

`\begin{gathered} 2x-10x+25=1 \\ -8x=1-25 \\ -8x=-24 \\ x=-(24)/(-8) \\ x=3 \end{gathered}`

Finally replace the calculated value of x in the first equation and solve for y

`\begin{gathered} y=2\cdot3-5 \\ y=1 \end{gathered}`

Using the second equation you can prove if the calculations are correct:

`\begin{gathered} 2x-5y=1 \\ \text{for x=3 and y=1 } \\ 2\cdot3-5\cdot1=6-5=1 \end{gathered}`

The calculations check, the values are x=3 and y=1