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Solve by elimination: x + (1/2)y = 6 and (3/2)x + (2/3)y = 17/2.
A(6, 3)
B(3, -6)
C(3, 6)
D(4, 4)
Answer & Solution
Correct answer: C. (3, 6)
1. Clear the fractions by multiplying each equation by its LCD: the first becomes 2x plus y equals 12, and the second becomes 9x plus 4y equals 51.
2. Multiply the first new equation by -4 to make the y-coefficients opposites: -8x minus 4y equals -48.
3. Add this to 9x plus 4y equals 51: x equals 3.
4. Substitute x = 3 into 2x + y = 12 to get y equals 6, giving the ordered pair (3, 6).
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.3 Solve Systems of Equations by Elimination_
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