Question

Without graphing, tell whether the graphs of the system of equations are parallel, perpendicular, intersecting or coinciding.

y = x + 7 and y = - x + 2
y = 5x and y = 5x - 1
2x + y = 1 and 2y + 4x = 2
y = 2x + 3 and y = -x - 4

Answer 1

Answer:

They must be in ax+by+c=0 form change all these into that form.

1. x-y+7=0 and x+y-2=0

a1= 1, a2= 1

b1= -1 , b2= 1

c1= 7, c2= -2

a1/a2 not equal to b1/b2 and a1a2+b1b2 =0

Hence they are interesting and perpendicular lines.

2. 5x-y =0 and 5x -y-1 =0

a1 =5, a2 = 5

b1 = -1 , b2 = -1

c1 =0 ,c2 = -1

a1/a2 =b1/b2 not equal to c1/c2

Hence they are parallel lines.

3. 2x+y-1=0 and 4x+2y-2 =0

a1= 2, a2 =4

b1 =1 , b2 =2

c1 =-1, c2 = -2

a1/a2 = b1/b2 = c1/c2

Hence they are coinciding lines.

4. 2x-y+3=0 and x+y+4=0

a1 = 2 , a2 =1

b1= -1 , b2 = 1

c1 = 3, c2 =4

a1/a2 not equal to b1/b2.

Hence they are intersecting lines.