Which of the following ordered pairs represents the solution to the system given below?
2x + y = 20
4x − 2y = 40
A. (10, 0)*****
B. (0, 10)
C.(4, 2)
D. (10, −10)
Check my work please!
THE ANSWER IS A because I go to FLVS
Yes, A.
To check which of the given ordered pairs represents the solution to the system of equations, we need to substitute the values of x and y from each ordered pair into both equations and check if they satisfy both equations.
Let's check each option one by one:
A. (10, 0)
Substituting x = 10 and y = 0 into the equations:
2(10) + 0 = 20 --> 20 = 20 (Satisfied)
4(10) - 2(0) = 40 --> 40 = 40 (Satisfied)
B. (0, 10)
Substituting x = 0 and y = 10 into the equations:
2(0) + 10 = 20 --> 10 = 20 (Not satisfied)
4(0) - 2(10) = 40 --> -20 = 40 (Not satisfied)
C. (4, 2)
Substituting x = 4 and y = 2 into the equations:
2(4) + 2 = 20 --> 10 = 20 (Not satisfied)
4(4) - 2(2) = 40 --> 32 - 4 = 40 --> 28 = 40 (Not satisfied)
D. (10, -10)
Substituting x = 10 and y = -10 into the equations:
2(10) - 10 = 20 --> 20 = 20 (Satisfied)
4(10) - 2(-10) = 40 --> 40 - (-20) = 40 --> 60 = 40 (Not satisfied)
So, the correct answer is A. (10, 0).
To find the solution to the system of equations, we can use the method of substitution or elimination. Let's use the substitution method in this case.
1. Start with the given system of equations:
2x + y = 20 -- (Equation 1)
4x − 2y = 40 -- (Equation 2)
2. Solve Equation 1 for y:
y = 20 - 2x
3. Substitute this value of y into Equation 2:
4x - 2(20 - 2x) = 40
4. Simplify and solve for x:
4x - 40 + 4x = 40
8x - 40 = 40
8x = 80
x = 10
5. Substitute the value of x back into Equation 1 to find y:
2(10) + y = 20
20 + y = 20
y = 0
Therefore, the solution to the system of equations is (10, 0). Option A: (10, 0) is the correct answer.