ASVAB CampSystems and Relationships flashcards
8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.
Term · 1/8
What is the solution of a system of two linear equations?
The ordered pair (x, y) that makes both equations true at the same time; on a graph it is the point where the two lines cross. List x first, then y.
Strategy · 2/8
When is substitution the best method for a system?
When one variable is already alone, or has coefficient 1 or −1 and is easy to isolate. For y = x + 2 and 3x + y = 14: 3x + x + 2 = 14, so x = 3 and y = 5.
Strategy · 3/8
How does the elimination method work?
Add the equations when a variable has opposite coefficients, subtract when they are equal, or scale one equation first. x + y = 9 and x − y = 3: adding gives 2x = 12, so x = 6 and y = 3.
Common trap · 4/8
Common errors when scaling or subtracting equations?
Multiplying only the targeted term instead of every term on both sides, and subtracting only the first term instead of every term, constants included. Both break the equality.
Fact · 5/8
How many solutions can a linear system have?
Exactly one (the lines cross), none (the lines are parallel), or infinitely many (both equations describe the same line). It can never have exactly two.
Rule · 6/8
How do slope and intercept classify a system?
In y = mx + b form: different slopes mean one solution; equal slopes with different intercepts mean none; equal slopes and intercepts mean infinitely many. Elimination ending in 0 = 0 means infinite; 0 = 4 means none.
Formula · 7/8
Two numbers have sum S and difference D. What are they?
Larger and smaller . With sum 40 and difference 12, the numbers are 26 and 14.
Strategy · 8/8
The question asks for x + y. Must you find x and y separately?
Not always. Combining the equations may give it directly: 2x + y = 11 plus x + 2y = 10 gives 3x + 3y = 21, so x + y = 7. Always answer exactly what is asked.