Mathematics

Question

PLEASE HELP!!

What is the point of intersection when the system of equations below is graphed on the coordinate plane?

X-Y=1
y-x=1

no intersection point
infinite intersection points
(1, 0)
(–1, 0)

2 Answer

  • No intersection point, First choice
  • Answer:  First option is correct.

    Step-by-step explanation:

    Since we have given that

    [tex]x-y=1----------(1)\\\\y-x=1\\\\\implies x-y=-1-----------------(2)[/tex]

    So, we first check its consistency:

    [tex]a_1=1,b_1=-1,c_1=1\\\\a_2=1,b_2=-1,c_2=-1[/tex]

    So, [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}\\\\\frac{1}{1}=\frac{1}{1}\neq \frac{1}{-1}\\\\1=1\neq -1[/tex]

    So, it is the parallel lines.

    Hence, there is no intersection points.

    Therefore, First option is correct.

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