Question

Solve the system of equations by graphing. x+y=6 4x+y=20

Answer 1

The solution to the system of equations is
`(4.667,1.333)`

Step-by-step explanation:

Given that the two equations are
`x+y=6` and
`4x+y=20`

We need to determine the solution of the system of equations graphically.

Let us consider the equation
`x+y=6`

We shall plot the equation
`x+y=6` in the graph using the x and y intercepts.

Substituting
`x=0`, we get,
`y=6`

Substituting
`y=0`, we get,
`x=6`

Thus, the x and y intercepts of the equation
`x+y=6` are
`(6,0)` and
`(0,6)` respectively.

Hence, joining these two coordinates, we get, the line for the equation
`x+y=6`

Now, we shall consider the equation
`4x+y=20`

We shall plot the equation
`4x+y=20` in the graph using the x and y intercepts.

Substituting
`x=0`, we get,
`y=20`

Substituting
`y=0`, we get,
`x=5`

Thus, the x and y intercepts of the equation
`4x+y=20` are
`(0,5)` and
`(0,20)` respectively.

Hence, joining these two coordinates, we get, the line for the equation
`4x+y=20`

The solution to the system of equations is the point of intersection of these two lines.

Hence, the point of intersection of these two lines is
`(4.667,1.333)`

Therefore, the solution to the system of equations is
`(4.667,1.333)`

The image of the graph containing the solution is attached below: