Question

For each ordered pair, determine whether it is a solution to the system of equations.y=-3x+86x +2y=16Is it a solution?Х$?(x, y)YesNo(-5,0)(7, -13)(1,8)(-2, 14)Check

Answer 1

Given:

The system of equation is,

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

Simplify both the equation,

`\begin{gathered} y=-3x+8 \\ 3x+y-8=0\ldots\ldots\ldots\text{.}(1) \end{gathered}`

and,

`\begin{gathered} 6x+2y=16 \\ \text{Divide by 2 on both side} \\ (6x)/(2)+(2y)/(2)=(16)/(2) \\ 3x+y=8 \\ 3x+y-8=0\ldots\ldots\ldots.(2) \end{gathered}`

It is observed that both the equations of line are same. moreover the lines completely overlap.

It shows the system has infinitely many solutions.

Now check the points (-5,0) ,(7, -13),(1,8),(-2, 14) represents the solution of the given system of equation.

`\begin{gathered} \text{For }(7,-13) \\ \text{Put x=7 in }3x+y-8=0 \\ 3(7)+y-8=0 \\ 21-8+y=0 \\ y=-13 \end{gathered}`
`\begin{gathered} \text{For (-2,14)} \\ \text{Put x=-2 in }3x+y-8=0 \\ 3(-2)+y-8=0 \\ -6-8+y=0 \\ y=14 \end{gathered}`
`\begin{gathered} \text{For (1,8) ,Put x = 1} \\ 3x+y-8=0 \\ 3(1)+y-8=0 \\ y-5=0 \\ y=5 \\ \end{gathered}`

This is not the solution of the given system of equations as it does not satisfy the equation.

Also point ( -5,0) is also not the solution of the equation.

Answer:

The system of equation has infinitely many solution and point (7, -13) and (-2, 14) is the solution.