Find the point of intersection (if any) of the following pairs of lines: a) x – 2y +1=0 2x + 3y – 7 = 0 b) x-2y+11=0 -x+2y-13 = 0

Accepted Solution

Answer:a) (11/7, 9/7)b) There's no point of intersectionStep-by-step explanation:a) x - 2y + 1 = 02x + 3y - 7 = 0To find the point of intersection, we need to solve the system of equations Β and the result will be the point of intersection (x,y)[tex]x-2y+1=0\\x= 2y-1[/tex]Now we substitute x in the second equation: [tex]2x+3y-7=0\\2(2y-1)+3y-7=0\\4y-2+3y-7=0\\7y-9=0\\y=9/7[/tex]Now we substitute y in our first equation.[tex]x-2y+1=0\\x-2(9/7)+1=0\\x-18/7+1=0\\x=18/7-1\\x=11/7[/tex].The point of intersection is (11/7, 9/7)b) x -2y +11 =0-x + 2y - 13 =0We are going to follow the same procedure:[tex]x-2y+11=0\\x=2y-11[/tex][tex]-(2y-11)+2y-13=0\\-2y+11+2y-13=0\\0y=2\\0=2[/tex]Since this system of equations doesn't have a solution, the system has no point of intersection.