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)