Question

2х +8y = 16 -3х +6y = 30determine the number of solutions

Answer 1

Given: The system of equation below

`\begin{gathered} 2x+8y=16 \\ -3x+6y=30 \end{gathered}`

To Determine: The number of solutions

Solution

Combine the two equations and solve

`\begin{gathered} equation1:2x+8y=16 \\ equation2:-3x+6y=30 \end{gathered}`

Multiply equation by 3 and equation 2 by 2

`\begin{gathered} 3(2x+8y=16)=6x+24y=48==equation3 \\ 2(-3x+6y=30)=-6x+12y=60==equation4 \end{gathered}`

Add equation 3 and 4

`\begin{gathered} 6x-6x+24y+12y=48+60 \\ 36y=108 \\ y=(108)/(36) \\ y=3 \end{gathered}`

Substitute y in equation 1

`\begin{gathered} 2x+8y=16 \\ 2x+8(3)=16 \\ 2x+24=16 \\ 2x=16-24 \\ 2x=-8 \\ x=-(8)/(2) \\ x=-4 \end{gathered}`

Hence, x = -4, y = 3