Question

Consider the pair of linear equations below:
4x+6y=12
2x+3y=6

Part A: What is the relationship, if any, between the two equations ?

Part B: Does the system of equations have one solution,no solution,or infinitely many solutions?
Explain.

Part C: How can you verify your answers to Parts A and B by solving algebraically?

Answer 1

Lines would be coincident so infinitely many solutions .....

Answer 2

Hint: multiply both sides of the second equation by 2. What do you get?

Answer 3

can you show me ? @nikato

Answer 4

So multiplying 2 on the left side
Gives you
2(2x+3y)
Distribute and get
4x+6y

Now on the right
6(2)
And you get 12
So the new transformed second equation becomes
4x+6y=12
Does this make sense?

Answer 5

I remember taking this lol.

Answer 6

@nikato

Answer 7

i need help in part a. @nikato

Answer 8

Ok. Now compare the transformed second equation with the original first equation.
What do you see?

And you didn't answer me 30 mins ago

Answer 9

like terms @nikato

Answer 10

Look at equation A; { 4x+6y=12 } -- now look at equation B; { 2x+3y=6 }

Do you see something similar?

Answer 11

like terms

Answer 12

♦o♦ >.> No try again

Answer 13

The equations have the same solutions.

Answer 14

X_X well that killed my moment ;-;

Yes, equation A is the same as equation B because equation A is twice of equation B

(2x+3y=6 )* 2 = (2x * 2) + (3y * 2) = (6*2) = 4x + 6y = 12

The same as A, they lie on top of each other >.<

Answer 15

\[
4x+6y=12
\]Can you solve for \(y\).

Answer 16

@Selena2345

Answer 17

Or there's that method ^ :o