Question

How do you solve `12x+132=12x-100` by graphing?

Answer 1

Is this question correct?

There is no common point so no solution to this system of equations as presented.

Explanation:

`color(blue)("Important point to note before we start")`

Given: `12x+132=12x-100`

Subtract `12x` from both sides

`132=-100 color(red)(larr" This is untrue so no solution")`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question as if there is a system of equations")`

In circumstances such as this you would set both as equal to `y` so that you have the format of:

`12x+132=y_1=12x-100 color(red)(larr" This proves to be false")`

However, take a closer look at it. Notice that they both have

`12x+" some constant"`

Now consider the standardised form:

`y=mx+c` where `m` is the gradient.

`y_2=12x+132" "y_3=12x-100`
`y=mx+c" "y=mx+c`

The gradient of `m` is the same in both equations. So they both have the same gradient (slope)

`color(red)("They are parallel")`

As they have different starting points on the y-axis ( y-intercept ) they do not share a common point anywhere.

`color(red)("Thus there is no solution")`