Final answer:
The solution to the system of equations 2x - 3y = -11 and 2x + y = 9 is x = 2 and y = 5, found by using the elimination method and substituting back into the original equation.
Step-by-step explanation:
To solve the system of equations 2x - 3y = -11 and 2x + y = 9, we can use the substitution or elimination method. In this case, we can opt for elimination since the coefficients of x in both equations are the same. We start by multiplying the second equation by 3 to align the y terms:
- 3(2x + y = 9) → 6x + 3y = 27
Now we have our new pair of equations:
- Equation 1: 2x - 3y = -11
- Equation 2: 6x + 3y = 27
Next, we add both equations together to eliminate y:
- 2x - 3y + 6x + 3y = -11 + 27
Which simplifies to:
Dividing both sides by 8 gives us:
Substituting x = 2 into the second original equation 2x + y = 9:
- 2(2) + y = 9
- 4 + y = 9
- y = 9 - 4
- y = 5
Therefore, the solution to the system of equations is x = 2 and y = 5.