# Verify if the lines y= 2x-3 , y= 3x+5 , y= x-11 meet at one point

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### 2 Answers

Solving the system of equations y= 2x - 3 and y= 3x + 5, we have

2x - 3 = 3x + 5

=> x = -8

and y = -19

If the line y = x - 11 passes through (-8 , -19)

-19 + 8 should be equal to -11, which it is .

**This verifies that all three lines pass through (-8 , -19)**

Given the three lines:

y= 2x-3 .........(1)

y= 3x+5.........(2)

y= x-11..........(3)

First we will determine the point of intersection between the lines (1) and (2).

==> 2x-3 = 3x + 5

==> x = -8 => y= -19

Then the point of intersection for (1) and (2) is (-8, -19).

Now we will determine the intersection point between (1) and (3).

==> 2x-3 = x-11

==> x = -8 ==> x = -19

Then the intersection point is (-8,-19).

**Then all three lines meet at the same point which is (-8, -19).**