➕ Algebra 1 · Systems of Equations
Systems Word Problems flashcards
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All 14 flashcards at a glance
Card 1
What are the first two steps in solving a system word problem?
Define each variable in words (with units), then write one equation for each fact in the story. Two unknowns need two equations.
Card 2
Which is a good variable definition: “let x be tickets” or “let x be the number of adult tickets sold”?
The second one. It says which quantity x is and what its unit is. “Tickets” could mean a count, a price or a total cost.
Card 3
Pens cost 2 dollars each and notebooks cost 5 dollars each. You buy p pens and n notebooks for 31 dollars in all. Write the equation for the money.
2p + 5n = 31. Each term is price × number, and the unit is dollars.
Card 4
What is the difference between a count equation and a value equation?
A count equation adds how many things there are (the unit is the thing being counted), like p + n = 8. A value equation adds what each kind is worth (price or rate × number), like 2p + 5n = 31. Do not mix the two.
Card 5
When is substitution a natural choice for a word problem?
When one variable is already alone or easy to get alone, such as a count equation x + y = 40 (so y = 40 − x), or two cost formulas that both start with C =.
Card 6
When is elimination a natural choice for a word problem?
When both equations are in standard form Ax + By = C, especially when a variable's coefficients already match or are opposites, like b + c and b − c for a boat.
Card 7
What is a graph useful for in a word problem?
It shows the picture: where two plans cross and which is cheaper before and after. Treat a point read from a graph as an estimate until you confirm it by substituting.
Card 8
A fruit stand sold 16 pieces of fruit, apples at 2 dollars each and pears at 3 dollars each, for 41 dollars in all. How many pears were sold?
9 pears (and 7 apples). With a apples and p pears: a + p = 16 and 2a + 3p = 41. Substitute a = 16 − p: 32 − 2p + 3p = 41, so 32 + p = 41 and p = 9.
Card 9
Plan 1 costs 9 dollars plus 2 dollars per visit. Plan 2 costs 3 dollars plus 5 dollars per visit. After how many visits do they cost the same?
2 visits. Set 9 + 2v = 3 + 5v. Then 6 = 3v, so v = 2. Each plan costs 13 dollars then.
Card 10
You set two plan costs equal, 12 + 4t = 5 + 4t, and get 12 = 5. What does that mean?
No solution: the plans never cost the same. The monthly rates are equal, so the 7-dollar gap in the fees never changes (parallel lines).
Card 11
Why check the answer against the original story and not only in your equations?
Your equations are your translation. If a sentence was mistranslated, the equations are wrong and the check passes anyway. The story also catches answers that do not make sense, like 3.5 tickets.
Card 12
The algebra gives 3.5 tickets sold. What do you do?
Recheck the equations and the numbers in the problem. If they are right, the solution is nonviable: tickets are whole numbers, so the story as written is impossible. Do not just round.
Card 13
How should the final answer to a word problem be written?
As a full sentence in the story's words, with units, such as “She bought 3 pens and 5 notebooks.” Say what each number counts.
Card 14
In this lesson's SOLVED memory trick, what do the letters stand for?
Say what each variable means, One equation per fact, Look for the easiest method, Values (solve for both), Examine the answer in the story, Deliver a sentence with units.