Answer:
x = 4 and y = 3.
Explanation:
To solve the system of equations using elimination, we can eliminate one variable by multiplying one or both equations by appropriate constants so that the coefficients of either x or y will cancel out when added or subtracted. Let's use the second equation to eliminate y.
Multiply the second equation 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:
4x + 4y = 28
-12x - 4y = -60
Add the two equations together:
(4x + 4y) + (-12x - 4y) = 28 + (-60)
-8x = -32
Divide both sides of the equation by -8 to solve for x:
x = (-32) / (-8)
x = 4
Substitute the value of x back into one of the original equations (let's use the second equation):
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.