I found y from the line, so I put it wherever I saw x.
The student plugs the linear expression into the wrong variable. For example, when both equations already give y, the student puts the line into x instead of setting the two y-values equal.
The student sees substitution as replacing any letter with an expression. They are not matching the variable that the expression actually equals.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
Keeps only one root from the quadratic
What you might hear
I already got one answer, so I do not need the other factor.
After substitution gives a quadratic equation, the student solves for only one x-value and stops. They miss the second root that can give another solution point.
The student is using the habit from linear systems, where there is usually one answer. They do not expect a line and a parabola to give two x-values.
This one is not a slip to correct — the underlying idea needs re-teaching before more practice will help.
Does not turn roots into ordered pairs
What you might hear
The answers are x = 1 and x = 4, so I am done.
The student solves the quadratic and reports only the x-values, or writes points like (x, 0). They do not plug each x-value back in to find its matching y-value.
The student treats the quadratic roots as the final answer. They miss that a system solution must make both equations true as an ordered pair.
This one is not a slip to correct — the underlying idea needs re-teaching before more practice will help.
What to say when you see it
For each mistake above, Algo School gives you the words to say next — the specific response that corrects the thinking instead of just marking the answer wrong, plus practice aimed at that exact error.
A linear-quadratic system is graphed as a line and a parabola. Using only the graph, how many solutions does the linear-quadratic system have? Which statement is correct?
AThe line does not meet the parabola, so the system has no solution.
BThe line crosses the parabola at two points, so the system has two solutions.
CThe line is tangent to the parabola, so the system has exactly one solution.
DThe system has two solutions, because a line and a parabola always meet at two points.
AnswerC — The line is tangent to the parabola, so the system has exactly one solution.
Generated by systems-alg2, a deterministic question engine — not written by an AI, and verified before any child sees it.
FAQ
Questions parents ask about this
How do I know which of these mistakes my child is making?
Look at what they SAY, not just what they wrote. Each mistake above includes the phrasing a parent typically hears — that sentence is usually the giveaway. In Algo School, the tutor recognises these patterns while your child is working and adapts the session around the one it sees.
Is "Solve a linear-quadratic system by substitution" something children normally struggle with?
Yes. We track 3 distinct approved mistake patterns for this concept, each one written up because it recurs — not because it is unusual. A child making one of them is doing something systematic, which is far easier to fix than random errors.
What should I do once I know which mistake it is?
Respond to the thinking, not the answer. Algo School gives parents the specific wording for each mistake, then generates practice targeted at that error and shows you whether it actually cleared.
Where do these mistakes come from?
They are part of the same content library that drives practice: each one is reviewed and approved before it is used, and the Advanced Equations and Systems questions on this site are checked by an automated verification pass before a child is ever served them.
Related
Other places children go wrong
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