Question

Solve the following equations by the elimination method . Write answer as coordinate points. 1/5 x +y =6/5 and 1/10x + 3y = 7/10 show all steps

Answer 1

we have the system of equations

`\begin{gathered} (1)/(5)x+y=(6)/(5)\text{ ----> equation 1} \\ \\ (1)/(10)x+(1)/(3)y=(7)/(10)\text{ ----> equation 2} \end{gathered}`

Solve by elimination

Multiply equation 2 by -2 on both sides

`-2[(1)/(10)x+(1)/(3)y=(7)/(10)]---->-(1)/(5)x-(2)/(3)y=-(14)/(10)\text{ ---> equation 3}`

Adds equation 1 and equation 3

`\begin{gathered} \begin{equation*} (1)/(5)x+y=(6)/(5) \end{equation*} \\ \begin{equation*} -(1)/(5)x-(2)/(3)y=-(14)/(10) \end{equation*} \\ --------- \\ (1)/(3)y=(6)/(5)-(7)/(5) \\ \\ (1)/(3)y=-(1)/(5) \\ \\ y=-(3)/(5) \end{gathered}`

Find out the value of x

substitute the value of y in any equation

equation 1

`\begin{gathered} (1)/(5)x+(-(3)/(5))=(6)/(5) \\ \\ (1)/(5)x=(6)/(5)+(3)/(5) \\ \\ (1)/(5)x=(9)/(5) \\ \\ x=9 \end{gathered}`

therefore

The solution is the point (9,-3/5)