Answer: O (4, -4)
Explanation:
To solve the system of equations using elimination, we can multiply the second equation by -3 to eliminate the y term:
Original equations:
5x + 3y = 8 (Equation 1)
4x + y = 12 (Equation 2)
Multiply Equation 2 by -3:
-3(4x + y) = -3(12)
-12x - 3y = -36 (Equation 3)
Now we can add Equation 1 and Equation 3 to eliminate the y term:
(5x + 3y) + (-12x - 3y) = 8 + (-36)
Simplifying:
5x - 12x + 3y - 3y = 8 - 36
-7x = -28
Divide both sides by -7:
x = -28 / -7
x = 4
Now substitute the value of x back into either of the original equations, let's use Equation 2:
4(4) + y = 12
16 + y = 12
y = 12 - 16
y = -4
Therefore, the solution to the system of equations is x = 4 and y = -4.