Find the intersection point between the lines of equations: 2x-y+6=0 and 2x+3y-6=0 ​

Find the intersection point between the lines of equations:

2x-y+6=0 and 2x+3y-6=0 ​

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  1. Step-by-step explanation:

    The two equation will intersect each other at the point which will be the solution of the given two equations , and the given equations are ,

    [tex]\implies 2x -y +6=0\\\\\implies 2x + 3y -6=0[/tex]

    On subtracting the given equations we have,

    [tex]\implies -y – 3y +6 -(-6) = 0 \\\\\implies -4y = -12 \\\\\implies y = -12/-4\\\\\implies y = 3 [/tex]

    Put this value in any equation , we have ,

    [tex]\implies 2x -3 +6 =0\\\\\implies 2x = -3 \\\\\implies x =\dfrac{-3}{2} \\\\\implies x =-1.5 [/tex]

    Hence the lines will Intersect at ,

    [tex]\implies\underline{\underline{ Point=(-1.5, 3)}}[/tex]

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  2. for the first one x = 1/2 y-3″ and y
    =
    2
    x
    +
    6 and for the other one is x
    =  −
    3
    /2  y+
    3  and y=

    2
    /3  x
    +
    2

    how i did this Step 1: Add -3y to both sides.

    Step 2: Add 6 to both sides.

    Step 3: Divide both sides by 2.

    Reply

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