Linear #-># straight line plot
When in the form of #y=mx+c# and you compare them.
#m -># gradient (slope)
#c -># y-intercept (point where it crosses the y-axis)
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With two linear equations
If #m# is the same in each but #c# is not the same then
#color(white)("dddd")#Parallel so do not cross thus no shared point.
#color(white)("dddd")#This is called 'no solution'.
If both #m and c# are the same
#color(white)("dddd")#One is superimposed on the other (coincidental).
#color(white)("dddd")#This is called an' infinite count of solutions'.
If both #m and c# are different then they cross once.
#color(white)("dddd")#This has just one shared point so has 1 solution.
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Given equations:
#color(white)(d.)2x-5y=3" ".....................Equation(1)#
#-4x+10y=-6" "................Equation(2)#
Manipulation gives:
#y=2/5x-3/5" ".....................Equation(1_a)#
#y=2/5x-3/5" "........................Equation(2_a)#
Both #m and c# are the same so they are coincidental.
Thus there is an infinite count if solutions
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#color(blue)("Check")#
#(-2)xxEquation(1) -> -4x+10y=-6#
This is the same as #Equation(2)#
