Answer:
Step-by-step explanation:
4x + 6y = 12 .................... equation 1
2x + 3y = 6 .....................equation 2
from equation 2
2x + 3y = 6 .................. equation 2
2x = 6-3y
divide both sides by 2
2x/2=(6-3y)/2
x = (6-3y)/2.......................equation 3....this is the relationship between the two equation.
substitute for x in equation 1
4x + 6y = 12 .................... equation 1
4(6-3y)/2 = 12
2(6-3y) = 12
12 -6y = 12
12-12 = 6y
0=6y
divide both sides by 6
0/6 = 6y/6
y = 0
put y=0 in equation 3
x = (6-3y)/2
x = 6-3(0)/2
x = 6-0/2
x = 6/2
x = 3.
when one side of the equation is identical to the other side of the equation, then it is said to have an infinite form of solutions.that is x=x
so to check if the eqation is infinite, we check by inserting the values of x and y into the equation.
x = (6-3y)/2
3 = 6-3(0)/2
3 = 6-0/2
3 = 6/2
3=3
since 3=3 then the solution is infinite.
inorder to verify your answer algebracally is by putting the value of x and y in the question to check
from equation 1
4x + 6y = 12
note, y=0 , x = 3
4(3) + 6(0) = 12
12 +0 = 12
12=12................. proved
