What is the point of intersection of lines -2x+y-1 and x+y-5?

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samhouston's profile pic

samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted on

These are not equations of lines because there are no equal signs in the equations.

Assuming the equations are...

-2x + y = 1

x + y = 5

Set both equations to equal y.

-2x + y = 1               y = 1 + 2x

x + y = 5                  y = 5 - x

Since both equations equal y, then they equal each other.

1 + 2x = 5 - x

Solve for x.

1 + 3x = 5

3x = 4

x = 4/3

Now substitute 4/3 in for x in one of the equations and solve for y.

y = 5 - x

y = 5 - 4/3

y = 11/3

You can check this by substituting 4/3 for x and 11/3 for y in the other equation.

y =  1 + 2x

11/3 = 1 + 2 * 4/3

11/3 = 1 + 8/3

11/3 = 11/3     check!

Point of Intersection:  (4/3 , 11/3)

This question can also be solved graphically.  Rewrite both equations in slope-intercept form.

y = -1x + 5

y = 2x + 1

Graph both equations and find the point of intersection.

Notice that the point of intersection is (4/3, 11/3) or (`~~` 1.3, `~~` 3.7).

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The intercepting point of the given lines represents the solution of the system of equations of the lines.

We'll re-write the equation of the lines using slope intercept formula:

-2x+y-1=0 <=> y = 2x + 1 (1)

x+y-5 = 0 <=> y = -x + 5(2)

We'll equate (1) and (2):

2x + 1 = -x + 5

We'll isolate x to the left side moving the numbers alone to the right side:

2x + x = 5 - 1

3x = 4

x = 4/3

y = -4/3 + 5

y = 11/3

The intercepting point of the given lines is represented by the pair of coordinates (4/3 ; 11/3).

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