MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

Answer:The coordinates of the intersection point are [tex](7,-2)[/tex]Step-by-step explanation:we have[tex]x+y=5[/tex] -----> equation A[tex]2x-y=16[/tex] -----> equation B[tex]x+2y=3[/tex] -----> equation C we know thatIf the system of equations intersect at one point, then the system of equations has one solutionusing a graphing toolsee the attached figureThe coordinates of the intersection point are [tex](7,-2)[/tex]This point is a common solution for the three equationsVerifySubstitute the value of [tex]x=7, y=-2[/tex] in each equationsoEquation A[tex]x+y=5[/tex] [tex]7-2=5[/tex][tex]5=5[/tex] ----> is true, therefore the point is a solution of the equation AEquation B[tex]2x-y=16[/tex][tex]2(7)+2=16[/tex][tex]16=16[/tex] ----> is true, therefore the point is a solution of the equation BEquation C[tex]x+2y=3[/tex] [tex]7+2(-2)=3[/tex][tex]3=3[/tex] ----> is true, therefore the point is a solution of the equation C