Home › NY Regents Algebra I › Mathematics › Systems of Linear Equations › Solve by substitution: 2x + y = 7 and x - 2y = 6.
Solve by substitution: 2x + y = 7 and x - 2y = 6.
A(-1, 4)
B(4, 1)
C(4, -1)
D(2, 3)
Answer & Solution
Correct answer: C. (4, -1)
1. Solve the first equation for y: y equals 7 minus 2x.
2. Substitute this expression into the second equation: x minus 2(7 minus 2x) equals 6.
3. Distribute and simplify: x minus 14 plus 4x equals 6, so 5x equals 20, giving x equals 4.
4. Substitute x = 4 back into y = 7 - 2x to get y equals -1, and checking confirms both original equations hold at (4, -1).
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.2 Solve Systems of Equations by Substitution_
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