To solve this system of equations using the elimination method, we start by writing the two equations clearly:
- Equation 1: 3x + 4y = 9
- Equation 2: 3x + 2y = 9
Next, we notice that both equations have the term 3x. To eliminate x from the equations, we can subtract Equation 2 from Equation 1:
Subtracting Equation 2 from Equation 1:
(3x + 4y) - (3x + 2y) = 9 - 9
This simplifies to:
4y - 2y = 0
Which gives us:
2y = 0
Now, we can solve for y:
y = 0
Now that we have the value of y, we can substitute it back into one of the original equations to find x. We’ll use Equation 2 for this:
3x + 2(0) = 9
This simplifies to:
3x = 9
Now, divide both sides by 3:
x = 3
So, the solution to the system of equations is:
(x, y) = (3, 0)
In conclusion, by using the elimination method, we found that the solution to the system of equations is x = 3 and y = 0.