Answer: (4, 3)
Explanation:
To solve the system of equations using elimination, we can manipulate the equations to eliminate one variable and solve for the other.
Let's start with the given system of equations:
Equation 1: 4x + 4y = 28
Equation 2: 3x + y = 15
To eliminate the y variable, we can multiply Equation 2 by 4 to make the coefficients of y in both equations the same:
4 * (3x + y) = 4 * 15
12x + 4y = 60
Now we have two equations with the same coefficient for y:
Equation 1: 4x + 4y = 28
Equation 3: 12x + 4y = 60
We can subtract Equation 1 from Equation 3 to eliminate the y variable:
Equation 3 - Equation 1:
(12x + 4y) - (4x + 4y) = 60 - 28
12x - 4x = 32
8x = 32
x = 4
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use Equation 2:
3x + y = 15
3(4) + y = 15
12 + y = 15
y = 15 - 12
y = 3
Therefore, the solution to the system of equations is x = 4 and y = 3. So the answer is (4, 3).