Two lines represented by the equations y = x + 1 and y = 2x + 3

Question

Two lines represented by the equations  y=x+1  and  y=2x+3  intersect at point P. What are the coordinates of P?

A. (–2, –1)
B. (–1, 2)
C. (1, –2)
D. (2, –1)
E. (1, 2)

Kinshook · Answer

Given: Two lines represented by the equations  y=x+1  and  y=2x+3  intersect at point P. 
Asked: What are the coordinates of P?

At intersection point P: - 
y = x + 1 = 2x + 3
x = -2
y = -1
(x,y) = (-2,-1)

IMO A

sumitkrocks · Answer

Two lines represented by the equations y=x+1y=x+1 and y=2x+3y=2x+3 intersect at point P. What are the coordinates of P?

At P two equations shall fetch same coordinates

so, X+1=2x+3
X=-2
y=-1
Answer A

sankalp1992 · Answer

At the intersection point P, both the lines will have the same coordinates.

Check the options--> put the value of 'x' in both the equations (coordinates of x from the option) and solve for 'y'. If getting 'y' same as the coordinate of 'y' as given in the option, that's the correct option.

Option A is the correct (IMO)

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given 
 • two lines represented by the equations y=x+1 and y=2x+3
• these lines intersect at point P

To find  
We need to determine
 • The coordinates of P

Approach and Working out

• At the point of intersection, P, the equations of both the lines will be satisfied.
• We can solve this system of equations by substitution or elimination.
 o Substitution Method: 
  Put the value of y from equation 1(y = x + 1) into equation 2 (y = 2x + 3).
 • x + 1 = 2x + 3
• x = -2 
 Put x = -2 in any one equation to get y.
 • y = x + 1 = -2 + 1 = -1 
 The coordinates of P are (x, y) = (-2, -1)

Thus, option A is the correct answer.

Correct Answer: Option A

ScottTargetTestPrep · Answer

Solution:
 
We can set the left-side expressions of the equations equal to each other (since they are both equal to y) and solve for x:

x + 1 = 2x + 3

-2 = x

We see that the x-coordinate of P is -2. Since only choice A has an x-coordinate of -2, it must be the correct answer.

Answer: A

Two lines represented by the equations y = x + 1 and y = 2x + 3

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GMAT Problem Solving (PS) Questions

Two lines represented by the equations y = x + 1 and y = 2x + 3

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