use the elimination method to solve the system of equations. Choose the correct ordered pair.
2x+4y=16
2x-4y=0
A.(4,2)
B.(2,4)
C.(2,-4)
D.(4,-2)
To solve this system of equations using the elimination method, we need to eliminate one of the variables. In this case, we can eliminate the variable 'x' by adding the two equations together.
Adding the equations:
(2x + 4y) + (2x - 4y) = 16 + 0
4x + 0y = 16
4x = 16
To isolate 'x', we divide both sides of the equation by 4:
4x/4 = 16/4
x = 4
Now that we know the value of 'x', we can substitute it back into one of the original equations. Let's use the first equation:
2x + 4y = 16
2(4) + 4y = 16
8 + 4y = 16
4y = 16 - 8
4y = 8
To solve for 'y', we divide both sides of the equation by 4:
4y/4 = 8/4
y = 2
Therefore, the correct ordered pair that satisfies both equations is (4, 2). So, the answer is:
A. (4, 2)
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. In this case, notice that if we add the two equations together, the y-terms will cancel out.
Adding the equations, we get:
(2x + 4y) + (2x - 4y) = 16 + 0
Combining like terms, we have:
4x = 16
To find the value of x, we divide both sides of the equation by 4:
4x / 4 = 16 / 4
x = 4
Now that we know the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
2x + 4y = 16
Substituting x = 4, we have:
2(4) + 4y = 16
Simplifying:
8 + 4y = 16
To isolate the variable y, we subtract 8 from both sides:
8 + 4y - 8 = 16 - 8
4y = 8
Dividing both sides by 4:
4y / 4 = 8 / 4
y = 2
Therefore, the correct ordered pair is (4,2), which corresponds to Option A.