Question

In the system of equations shown, a is the coefficient of x. The system has infinitely many solutions. What is the value of a? x – 2y = 4 ax– 6y = 12

Answer 1

x – 2y = 4

ax– 6y = 12

The second equation must has a value for a that makes the second equation equal to the first. In other words a has to be something that divides through the second equation to get the first.

The easiest way to proceed is to look at the right hand side. One equation has 12 on the right. The other has 4. What do you have to do to 12 to get it down to 4. I suppose you could subtract 8, but that would not apply to the left side.

The answer is divide 12 by 3.

If you do that then the 6 is divided by 3.

Find a

Now you need to consider a's value. It is either 1 or 3. If you choose 1, you will not be able to divide properly: dividing by 3 will leave you with 1/3.

The thing you must do is make a = 3

The second equation then becomes

3x - 6y = 12   Divide everything by 3

x - 2y = 12/3 = 4

Answer: a = 3