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.4x + 5y = 222x + 3y = 12A.(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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