Solve the system of equations and choose the correct ordered pair.4x + 5y = 222x + 3y = 12A.(2, 3)B.(4, 1)C.(4, 5)D.(3, 2)
Question
Solve the system of equations and choose the correct ordered pair.
A. (2, 3)
B. (4, 1)
C. (4, 5)
D. (3, 2)
Solution
To solve the system of equations, we can use the method of substitution or elimination. Here, I'll use the elimination method.
The system of equations is:
4x + 5y = 22 2x + 3y = 12
First, we can multiply the second equation by 2 to make the coefficients of x in both equations the same:
4x + 5y = 22 4x + 6y = 24
Now, subtract the second equation from the first:
(4x + 5y) - (4x + 6y) = 22 - 24 4x + 5y - 4x - 6y = -2 -y = -2
Divide both sides by -1 to solve for y:
y = 2
Substitute y = 2 into the first equation:
4x + 5(2) = 22 4x + 10 = 22 4x = 12 x = 3
So, the solution to the system of equations is (3, 2), which corresponds to answer choice D.
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