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Adding the equations 3x + y = 5 and 2x - y = 0 together eliminates y. What is the resulting solution?
A(2, 1)
B(1, -2)
C(1, 2)
D(-1, 2)
Answer & Solution
Correct answer: C. (1, 2)
1. Adding the two equations makes the y-terms cancel: 3x plus 2x equals 5x, and y plus -y equals 0.
2. The result is 5x equals 5, so x equals 1.
3. Substitute x = 1 into 2x - y = 0 to get 2 minus y equals 0, so y equals 2.
4. Check: 3(1) plus 2 equals 5, and 2(1) minus 2 equals 0, so (1, 2) satisfies both equations.
_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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