Question

Prove that the lines x+y=5, 2x–y=16 and x+2y=3 intersect at one point. What are the coordinates of this point?

Answer 1

The coordinates of the intersection point are
`(7,-2)`

Explanation:

we have

`x+y=5` -----> equation A

`2x-y=16` -----> equation B

`x+2y=3` -----> equation C

we know that

If the system of equations intersect at one point, then the system of equations has one solution

using a graphing tool

see the attached figure

The coordinates of the intersection point are
`(7,-2)`

This point is a common solution for the three equations

Verify

Substitute the value of
`x=7, y=-2` in each equation

so

Equation A

`x+y=5`

`7-2=5`

`5=5` ----> is true, therefore the point is a solution of the equation A

Equation B

`2x-y=16`

`2(7)+2=16`

`16=16` ----> is true, therefore the point is a solution of the equation B

Equation C

`x+2y=3`

`7+2(-2)=3`

`3=3` ----> is true, therefore the point is a solution of the equation C