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

Answer:

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

Step-by-step 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