Question

How do you solve the system of equations `y=11x-6` and `y=-6x+11` by graphing?

Answer 1

See a solution process below:

Explanation:

Graph Equation 1:

First, find two points to solve the first equation, plot the points and draw a straight line through the points:

For `x = 0`
`y = (11 * 0) - 6`
`y = 0 - 6`
`y = -6` or `(0, -6)`

For `x = 1`
`y = (11 * 1) - 6`
`y = 11 - 6`
`y = 5` or `(1, 5)`

graph{(y - 11x + 6)(x^2+(y+6)^2-0.1)((x-1)^2+(y-5)^2-0.1)=0 [-25, 25, -12.5, 12.5]}

Graph Equation 2:

First, find two points to solve the second equation, plot the points and draw a straight line through the points:

For `x = 0`
`y = (-6 * 0) + 11`
`y = 0 + 11`
`y = 11` or `(0, 11)`

For `x = 2`
`y = (-6 * 2) + 11`
`y = -12 + 11`
`y = -1` or `(2, -1)`

graph{(y+6x-11)(y - 11x + 6)(x^2+(y-11)^2-0.2)((x-2)^2+(y+1)^2-0.2)=0 [-30, 30, -15, 15]}

The Solution Is:

graph{(y+6x-11)(y - 11x + 6)((x-1)^2+(y-5)^2-0.05)=0 [-2, 22, -2, 10]}

`(1, 5)`