Question

the equation of lime 1 is 3x-2y=5, and the equation of lime 2 is x+2y=7. What is the point of intersection of the two lines?

Answer 1

Points of Intersection

To find the point of intersection for two lines, we can use substitution to solve for the coordinates.

Solving the Question

We're given:

• 
  `3x-2y=5`
• 
  `x+2y=7`

With these two equations, we can:

1. First isolate x in the second equation
2. Use substitution to input in second equation into the first and solve for y
3. Use the y-coordinate to find the corresponding x-coordinate using substitution

Isolate x in the second equation:

`x+2y=7\\x =7-2y`

Substitute the second equation into the first:

`3x-2y=5\\3(7-2y)-2y=5\\21-6y-2y=5\\21-8y=5\\21-8y=5`

Solve for y:

`21-6y-2y=5\\21-8y=5\\-8y=-16\\y=2`

Solve for x:

`x+2y=7\\x+2(2)=7\\x+4=7\\x=3`

Answer

The point of intersection of the lines is (3,2).