Answer:
Inconsistent= 1, & 3
Equivalent= 2&6
Consistent= 4&5
Explanation:
Equivalent means both sides of the equation has similar results
Consistent means the equation has an order pair of x, y that make it true
Inconsistent means impossible to solve using a set of values for the variable
1. y=3x-2
3x-y=4----------------make y subject of equation as 3x-4=y
Equate the two equation
y=3x-2
y=3x-4
3x-2=3x-4---------------collect like terms
3x-3x=-4+2
0=-2---------------inconsistent
2. 1/2 y=-x+5------------multiply by 2 both sides to have y=-2x+10
2y=-4x+2
we have
y=-2x+10----------------------use y in this equation in the second equation
2y=-4x+20
2(-2x+10)=-4x+20
-4x+20=-4x+20----------------Equivalent
3. y=-x+4----------------use this in the second equation as
x=-y-6
x= - (-x+4)-6
x= x-4-6
x=x-10--------------collect like terms
x-x= -10
0= -10--------------inconsistent
4. y=4x+2
y=6x-10-----------equate the two
4x+2=6x-10----------collect like terms
4x-6x=-10-2
-2x=-12
x=6---------------------use to find y
y=4(6)+2=24+2=26
(x,y)=(6,26)---------consistent
5. y=2x+1
y=-2x+3
Equate the two equation
2x+1=-2x+3-------------collect like terms
2x+2x=3-1
4x=2
x=1/2----------use to find y
y=2 *1/2 +1 =1+1=2
(x,y) = (1/2, 2)---------------consistent
6. -2x +5y=0
y=2/5x-------------------use this in the first equation
-2x + 5(2/5 x)=0
-2x+2x =0
0=0-----------------------Equivalent