Home › NY Regents Algebra I › Mathematics › Systems of Linear Equations › Solve by substitution: 4x + 2y = 4 and 6x - y = 8.
Solve by substitution: 4x + 2y = 4 and 6x - y = 8.
A(-1/2, 5/4)
B(5/4, 1/2)
C(1/4, -1/2)
D(5/4, -1/2)
Answer & Solution
Correct answer: D. (5/4, -1/2)
1. Solve the second equation for y: y equals 6x minus 8.
2. Substitute into the first equation: 4x plus 2(6x minus 8) equals 4.
3. Distribute and simplify: 4x plus 12x minus 16 equals 4, so 16x equals 20, giving x equals five-fourths.
4. Substitute x = 5/4 into y = 6x - 8 to get y equals negative one-half, giving the ordered pair (5/4, -1/2).
_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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