Answer:
Explanation:
To eliminate the x term in the system of equations, you can multiply Equation P by a constant and then add or subtract it from Equation Q. Let's go through the given steps:
2(x + y = 8):
This step is incorrect because it only multiplies the entire Equation P by 2 without changing the other equation. It does not eliminate the x term.
-2(x + y = 8):
This step is incorrect because it multiplies Equation P by -2, but the equation should be subtracted from Equation Q, not multiplied by -2.
-1(2x + 5y = 24):
This step is incorrect because it only multiplies Equation Q by -1 without changing Equation P. It does not eliminate the x term.
-2(2x + 5y = 24):
This step is correct. By multiplying Equation Q by -2 and then adding it to Equation P, the x term will be eliminated. The resulting equation will involve only the y term, allowing you to solve for y.
Therefore, the correct step to eliminate the x term is -2(2x + 5y = 24).
To prove that the step -2(2x + 5y = 24) eliminates the x term in the system of equations, we need to show that when we perform the elimination, the resulting equation involves only the y term.
Given the system of equations:
Equation P: x + y = 8
Equation Q: 2x + 5y = 24
Multiplying Equation Q by -2:
-2(2x + 5y) = -2(24)
-4x - 10y = -48
Now, let's add Equation P and the modified Equation Q:
(x + y) + (-4x - 10y) = 8 + (-48)
Simplifying the left side of the equation:
x - 4x + y - 10y = 8 - 48
-3x - 9y = -40
As we can see, the resulting equation -3x - 9y = -40 involves only the y term. The x term has been eliminated.
Therefore, by performing the step -2(2x + 5y = 24), we have successfully eliminated the x term in the system of equations.