Final answer:
By using the elimination method, the system of equations 2x+3y=16 and 0.5x+0.7y=-4 is solved to find that x = 248 and y = 160.
Step-by-step explanation:
To solve the system of equations 2x+3y=16 and 0.5x+0.7y=-4 using the elimination method, we first need to manipulate the equations so that when they are added together, one of the variables will be eliminated.
Let's multiply both sides of the second equation by 4 to make the coefficient of x in both equations the same:
2x + 3y = 16
(0.5x + 0.7y) × 4 —> 2x + 2.8y = -16
Now, if we subtract the second equation from the first, 2.8y will be eliminated:
(2x + 3y) - (2x + 2.8y) = 16 - (-16)
2x - 2x + 3y - 2.8y = 32
0.2y = 32
Divide by 0.2 to find y:
y = 32 / 0.2
y = 160
Now, plug the value of y into the first equation to find x:
2x + 3(×160) = 16
2x - 480 = 16
2x = 16 + 480
2x = 496
x = 496 / 2
x = 248
Therefore, the solution to the system of equations is x = 248 and y = 160.