# 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. ThanhThu

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]

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.