Home › NY Regents Algebra I › Mathematics › Systems of Linear Equations › Solve by substitution: 4x - 3y = 6 and 15y - 20x…
Solve by substitution: 4x - 3y = 6 and 15y - 20x = -30.
AInfinitely many solutions, since the equations are dependent
BExactly one solution, at the point (6, 6)
CNo solution, since the equations are inconsistent
DExactly one solution, at the point (0, -2)
Answer & Solution
Correct answer: A. Infinitely many solutions, since the equations are dependent
1. Solve the first equation for x: x equals three-fourths y plus three-halves.
2. Substitute this expression into the second equation and simplify the result.
3. The variable terms cancel out entirely, leaving the true statement 0 equals 0.
4. Since the result is always true, the system is consistent but the equations are dependent, meaning it has infinitely many solutions.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.2 Solve Systems of Equations by Substitution_
Related questions
The perimeter of a rectangle is 40. The length is 4 more than the width. Find the length aThe sum of two numbers is 10. One number is 4 less than the other. Find the numbers.When Jenna spent 10 minutes on the elliptical and 20 minutes on circuit training, she burnA married couple together earns $110,000 a year. The wife earns $16,000 less than twice whDevon is 26 years older than his son Cooper. The sum of their ages is 50. Find their ages.In the seven-step Problem Solving Strategy for Systems of Linear Equations, what is Step 4Joe had one medium fries and two small sodas for 620 calories on Monday, and two medium frThe sum of two numbers is 39. Their difference is 9. Find the numbers.