Home › NY Regents Algebra I › Mathematics › Systems of Linear Equations › Without graphing, classify the system 2x + y = -…
Without graphing, classify the system 2x + y = -3 and x - 5y = 5.
ANo solution; inconsistent and independent
BInfinitely many solutions; consistent and dependent
COne solution; consistent and independent
DOne solution; consistent and dependent
Answer & Solution
Correct answer: C. One solution; consistent and independent
1. Rewrite both equations in slope-intercept form: the first becomes y equals -2x minus 3, and the second becomes y equals one-fifth x minus 1.
2. Compare the slopes: -2 and one-fifth are different, so the lines are neither parallel nor coincident.
3. Lines with different slopes always intersect at exactly one point.
4. A system whose lines intersect has one solution and is classified as consistent and independent.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.1 Solve Systems of Equations by Graphing_
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.