4x + 6y = 12 and 2x + 3y = 6 What is the relationship, if any, between the two equations? Does the system of equations have one solution, no solution, or in finitely many solutions? explain. how can u verify your answers to the two questions above by solving algebraically?

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