Question

Without graphing, determine the number of solutions to the system of equations.

{6x−4y=9, 12x−8y=18
Select the correct answer below:


no solution

one solution

infinitely many solutions

Answer 1

Infinitely Many Solutions!!

Explanation:

You need to do elimination method!!

This is because we need to top the equation to cancel out and become negative.

6x−4y=9

12x−8y=18

You could do 6x and everything multiplied by -2. But 4y can do the same too!!

I rather do 4y x -2!

-12x+8y=-18

12x−8y=18

Everything cancels out!!

0=0

But 0 equals to 0 goes on forever so the answer is infinite solutions!!

**The reasoning behind the two other choices**

No solution would be like -3=0 which is not our case!!

One solution has something that goes into everything evenly!

Answer 2

Infinitely many solutions

Explanation:

(1) ---- 6x - 4y = 9

(2)---- 12x - 8y = 18

If you multiply (1) by 2 → 12x - 8y = 18 --- (3)

and then when you compare (2) and (3), you'll find that you still can't find the value of X and Y therefore, there's infinitely many solutions