SAT Exam > SAT Questions > 3x+ 4y = 18y = 3/2xWhich of the following ord...
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3x+ 4y = 18
y = 3/2x
Which of the following ordered pairs (x, y) is a solution of the system of equations above?
y = 3/2x
Which of the following ordered pairs (x, y) is a solution of the system of equations above?
- a)(2, 3)
- b)(3, 2.25)
- c)(4, 1.5)
- d)(4, 6)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
3x+ 4y = 18y = 3/2xWhich of the following ordered pairs (x, y) is a so...
To determine which ordered pair is a solution to the system, just “plug in” the values for x and y and choose the one that satisfies both equations. Notice that x = 2 and y = 3 is a solution because 3(2) + 4(3) = 18, and 3 = (3/2)(2)
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3x+ 4y = 18y = 3/2xWhich of the following ordered pairs (x, y) is a so...
Understanding the System of Equations
To solve the system of equations given:
1. 3x + 4y = 18
2. y = (3/2)x
We need to find which of the ordered pairs provided satisfies both equations.
Substituting y in the First Equation
- From the second equation, substitute y in the first equation:
3x + 4((3/2)x) = 18
- Simplifying this gives:
3x + 6x = 18
9x = 18
x = 2
- Now, substituting x back into the second equation to find y:
y = (3/2)(2) = 3
Thus, the solution to the system is (2, 3).
Checking the Ordered Pairs
Now, we will check each ordered pair to see if they satisfy both equations:
- (2, 3):
- 3(2) + 4(3) = 6 + 12 = 18 (satisfies 1st equation)
- y = (3/2)(2) = 3 (satisfies 2nd equation)
- (3, 2.25):
- 3(3) + 4(2.25) = 9 + 9 = 18 (satisfies 1st equation)
- y = (3/2)(3) = 4.5 (does not satisfy 2nd equation)
- (4, 1.5):
- 3(4) + 4(1.5) = 12 + 6 = 18 (satisfies 1st equation)
- y = (3/2)(4) = 6 (does not satisfy 2nd equation)
- (4, 6):
- 3(4) + 4(6) = 12 + 24 = 36 (does not satisfy 1st equation)
Conclusion
Only the ordered pair (2, 3) meets the criteria for both equations, confirming that option A is indeed the correct answer.
To solve the system of equations given:
1. 3x + 4y = 18
2. y = (3/2)x
We need to find which of the ordered pairs provided satisfies both equations.
Substituting y in the First Equation
- From the second equation, substitute y in the first equation:
3x + 4((3/2)x) = 18
- Simplifying this gives:
3x + 6x = 18
9x = 18
x = 2
- Now, substituting x back into the second equation to find y:
y = (3/2)(2) = 3
Thus, the solution to the system is (2, 3).
Checking the Ordered Pairs
Now, we will check each ordered pair to see if they satisfy both equations:
- (2, 3):
- 3(2) + 4(3) = 6 + 12 = 18 (satisfies 1st equation)
- y = (3/2)(2) = 3 (satisfies 2nd equation)
- (3, 2.25):
- 3(3) + 4(2.25) = 9 + 9 = 18 (satisfies 1st equation)
- y = (3/2)(3) = 4.5 (does not satisfy 2nd equation)
- (4, 1.5):
- 3(4) + 4(1.5) = 12 + 6 = 18 (satisfies 1st equation)
- y = (3/2)(4) = 6 (does not satisfy 2nd equation)
- (4, 6):
- 3(4) + 4(6) = 12 + 24 = 36 (does not satisfy 1st equation)
Conclusion
Only the ordered pair (2, 3) meets the criteria for both equations, confirming that option A is indeed the correct answer.
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