color(blue)("Important point to note before we start")Important point to note before we start
Given: 12x+132=12x-10012x+132=12x−100
Subtract 12x12x from both sides
132=-100 color(red)(larr" This is untrue so no solution")132=−100← This is untrue so no solution
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color(blue)("Answering the question as if there is a system of equations")Answering the question as if there is a system of equations
In circumstances such as this you would set both as equal to yy so that you have the format of:
12x+132=y_1=12x-100 color(red)(larr" This proves to be false")12x+132=y1=12x−100← This proves to be false
However, take a closer look at it. Notice that they both have
12x+" some constant"12x+ some constant
Now consider the standardised form:
y=mx+cy=mx+c where mm is the gradient.
y_2=12x+132" "y_3=12x-100y2=12x+132 y3=12x−100
y=mx+c" "y=mx+cy=mx+c y=mx+c
The gradient of mm is the same in both equations. So they both have the same gradient (slope)
color(red)("They are parallel")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")Thus there is no solution
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