# Solving Straight Lines Homework: Find Intersection Point

• xiphoid
In summary, the equation "ix+(i+1)y+(i+2)=0; i=1,2" can be solved by replacing the values of i with 1 or 2, resulting in two equations: x+2y+3=0 and 2x+3y+4=0. These equations can then be solved to find the point of intersection between the two lines.
xiphoid

## Homework Statement

Lines li: ix+(i+1)y+(i+2)=0; i=1,2 intersect at___ point?

## Homework Equations

The equation is required at first!

## The Attempt at a Solution

I am confused!
How and where should I replace the values of i with 1 or 2?
This is the first step but i am unable to do...

You are given "ix+(i+1)y+(i+2)=0; i=1,2". You replace those "i"s by 1 and 2!

i= 1: 1x+ (1+1)y+ (1+2)= x+ 2y+ 3= 0
i= 2: 2x+ (2+1)y+ (2+ 2)= 2x+ 3y+ 4= 0

Thanks!
HallsofIvy said:
You are given "ix+(i+1)y+(i+2)=0; i=1,2". You replace those "i"s by 1 and 2!

i= 1: 1x+ (1+1)y+ (1+2)= x+ 2y+ 3= 0
i= 2: 2x+ (2+1)y+ (2+ 2)= 2x+ 3y+ 4= 0

## 1. What is the purpose of finding the intersection point of two straight lines?

The intersection point of two straight lines is the point where the two lines intersect or cross each other. It is useful in various real-life applications such as engineering, architecture, and navigation. Solving for the intersection point can help determine the position, direction, and relationship between two lines, which can be used to make accurate calculations and predictions.

## 2. How do you find the intersection point of two straight lines?

To find the intersection point of two straight lines, you can use the method of substitution or elimination. In substitution, you solve one equation for one variable and substitute the value into the other equation. In elimination, you manipulate the equations to eliminate one variable and solve for the other. Once you have the values of both variables, you can plug them into the equations to find the intersection point.

## 3. Can you find the intersection point if the lines are parallel or coincident?

No, it is not possible to find the intersection point if the lines are parallel or coincident. Parallel lines have the same slope, so they will never intersect. Coincident lines are the same line, so they have an infinite number of intersection points. In both cases, you will end up with an inconsistent system of equations, and there will be no solution for the intersection point.

## 4. What if the lines are not given in standard form?

If the lines are not given in standard form (y=mx+b), you can rewrite them in that form by rearranging the equations. For example, if the lines are given in slope-intercept form (y=mx+b), you can solve for y and get it in the form y=mx+b. Once both lines are in standard form, you can use the methods mentioned in question 2 to find the intersection point.

## 5. Is there a shortcut or formula for finding the intersection point?

Yes, there is a formula for finding the intersection point of two lines given in standard form. The formula is x = (b2-b1)/(m1-m2), where b1 and b2 are the y-intercepts and m1 and m2 are the slopes of the two lines. However, it is still important to understand the concept and methods of solving for the intersection point in case the lines are not in standard form or the formula is not applicable.

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