Point of Intersection of two lines calculator

SolutionMethods

1. Find the point of intersection of the lines

$x+y=1$ and

$x-y=1$

2. Find the point of intersection of the lines

$3y+1=0$ and

$x+y-2=0$

3. Find the point of intersection of the lines

$x-y+1=0$ and

$2x-3y+5=0$

4. Find the point of intersection of the lines

$2x+y-5=0$ and

$x+y-3=0$

5. Find the point of intersection of the lines

$x-2y+15=0$ and

$3x+y-4=0$

6. Find the point of intersection of the lines

$5x+2y-11=0$ and

$3x-y+11=0$

Example

1. Find the point of intersection of the lines $x+y=1$ and $x-y=1$

Solution:
The point of intersection of the lines can be obtainted by solving the given equations

$x+y=1$

and

$x-y=1$

$x+y=1 ->(1)$

$x-y=1 ->(2)$

Substracting

$=>2y=0$

$=>y=0/2$

$=>y=0$

Putting

$y=0$ in equation

$(1)$ , we have

$x+0=1$

$=>x=1$

$:.x=1" and "y=0$

$:. (1,0)$ is the intersection point of the given two lines.

2. Find the point of intersection of the lines $3y+1=0$ and $x+y-2=0$

Solution:
The point of intersection of the lines can be obtainted by solving the given equations

$3y+1=0$

$:.3y=-1$

and

$x+y-2=0$

$:.x+y=2$

$3y=-1 ->(1)$

$x+y=2 ->(2)$

Taking equation

$(1)$ , we have

$=>3y=-1$

$=>y=(-1)/3 ->(3)$

Putting

$y=(-1)/3$ in equation

$(2)$ , we get

$=>x+y=2$

$=>x+((-1)/3)=2$

$=>3x-1=6$

$=>3x=6+1$

$=>3x=7$

$=>x=7/3$

$:.y=-1/3" and "x=7/3$

$:. (7/3,-1/3)$ is the intersection point of the given two lines.

3. Find the point of intersection of the lines $x-y+1=0$ and $2x-3y+5=0$

Solution:
The point of intersection of the lines can be obtainted by solving the given equations

$x-y+1=0$

$:.x-y=-1$

and

$2x-3y+5=0$

$:.2x-3y=-5$

$x-y=-1 ->(1)$

$2x-3y=-5 ->(2)$

equation

$(1) xx 2 =>2x-2y=-2$

equation

$(2) xx 1 =>2x-3y=-5$

Substracting

$=>y=3$

Putting

$y=3$ in equation

$(1)$ , we have

$x-(3)=-1$

$=>x=-1+3$

$=>x=2$

$:.x=2" and "y=3$

$:. (2,3)$ is the intersection point of the given two lines.

4. Find the point of intersection of the lines $2x+y-5=0$ and $x+y-3=0$

Solution:
The point of intersection of the lines can be obtainted by solving the given equations

$2x+y-5=0$

$:.2x+y=5$

and

$x+y-3=0$

$:.x+y=3$

$2x+y=5 ->(1)$

$x+y=3 ->(2)$

Substracting

$=>x=2$

Putting

$x=2$ in equation

$(2)$ , we have

$2+y=3$

$=>y=3-2$

$=>y=1$

$:.x=2" and "y=1$

$:. (2,1)$ is the intersection point of the given two lines.

5. Find the point of intersection of the lines $x-2y+15=0$ and $3x+y-4=0$

Solution:
The point of intersection of the lines can be obtainted by solving the given equations

$x-2y+15=0$

$:.x-2y=-15$

and

$3x+y-4=0$

$:.3x+y=4$

$x-2y=-15 ->(1)$

$3x+y=4 ->(2)$

equation

$(1) xx 1 =>x-2y=-15$

equation

$(2) xx 2 =>6x+2y=8$

Adding

$=>7x=-7$

$=>x=-7/7$

$=>x=-1$

Putting

$x=-1$ in equation

$(1)$ , we have

$-1-2y=-15$

$=>-2y=-15+1$

$=>-2y=-14$

$=>y=7$

$:.x=-1" and "y=7$

$:. (-1,7)$ is the intersection point of the given two lines.

2. Find the point of intersection of the lines $5x+2y-11=0$ and $3x-y+11=0$

Solution:
The point of intersection of the lines can be obtainted by solving the given equations

$5x+2y-11=0$

$:.5x+2y=11$

and

$3x-y+11=0$

$:.3x-y=-11$

$5x+2y=11 ->(1)$

$3x-y=-11 ->(2)$

equation

$(1) xx 1 =>5x+2y=11$

equation

$(2) xx 2 =>6x-2y=-22$

Adding

$=>11x=-11$

$=>x=-11/11$

$=>x=-1$

Putting

$x=-1$ in equation

$(2)$ , we have

$3(-1)-y=-11$

$=>-y=-11+3$

$=>-y=-8$

$=>y=8$

$:.x=-1" and "y=8$

$:. (-1,8)$ is the intersection point of the given two lines.