Mathematics

Question

Choose the correct graph of the given system of equations.

y + 2x = −1
3y − x = 4

graph of two lines that intersect at the point (negative 1, 1)
graph of two lines that intersect at the point (1, 1) < Not
graph of two parallel lines with positive slopes
None of the above

2 Answer

  • Answer: Graph of two lines that intersect at the point (negative 1, 1).

    Step-by-step explanation:

    The given system of linear equations :

    [tex]y+2x=-1---------(1)\\\\3y-x=4-------------(2)[/tex]

    Multiply equation (1) by 3 , we get

    [tex]3y+6x=-3-------------(3)[/tex]

    Subtract equation (2) from (3), we get

    [tex]6x+x=-3-4\\\\ 7x=-7[/tex]

    Divide both sides by 7 , we get

    x=-1

    Put value of x in (1), we get

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

    ⇒ both lines are intersecting at (x,y)=(-1,1)

    ∴  The correct graph of the given system of equations : graph of two lines that intersect at the point (negative 1, 1)

  • Answer:

    (-1,1) One solution

    Step-by-step explanation:

    Use these steps for the equations:

    1)  Rewrite the equation in slope intercept form.

    2) Graph the first equation.

    3) Graph the second equation.

    4) Identify the point of intersection.

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