Question

Instructions: Determine the solution to the given system using the graph.System

Answer 1

Given:

`x+18-2y=0`
`3x=-54+6y`

Required:

We need to find the solution to the given system of equations.

Step-by-step explanation:

We need to find points that lie in the given system of equations,

Consider the equation.

`x+18-2y=0`

Set x =0 and substitute in the equation.

`0+18-2y=0`

`18=2y`
`(18)/(2)-(2y)/(2)`
`9=y`

We get (0,9).

Set y =4 and substitute in the equation.

`x+18-2(4)=0`
`x+18-8=0`
`x+10=0`
`x=-10`

We get (-10,4).

Mark the points (0,9) and (-10,4) on the graph and join them by ray.

Consider the equation.

`3x=-54+6y`

Set x =0 and substitute in the equation.

`3(0)=-54+6y`
`54=-54+6y+54`
`54=6y`

Divide both sides by 6.

`(54)/(6)=(6y)/(6)`
`9=y`

We get (0,9).

Set y=4 and substitute in the equation.

`3x=-54+6(4)`

`3x=-54+24`

`3x=-30`

`x=-(30)/(3)`
`x=-10`

We get (-10,4).

Mark the points (0,9) and (10,4) and join them by ray.

This line is the same as the first line.

Both equations give the same line.

Each point on the line is known as the solution to the given system of equations.

Final answer:

Infinite number of solutions.