MathGrade 8ages 13–14
⚖️ A system of equations
A system of equations asks for one pair of numbers that makes two sentences true at the same time — and a child who solves only the first equation has not actually solved the system.
Try this lesson freeNo card needed. The first lesson is free.
Download on the App StoreWhat your child learns
- A system is two equations that are true at the same time.
- The answer must satisfy both, so an answer to one alone is not an answer at all.
- In substitution one unknown is expressed and pushed into the other equation, leaving a single unknown.
- At the end the pair is checked in both original equations.
The mistake most kids make here
Solving one equation and ignoring the other.
Try one question
What must a system's answer satisfy?
What the answer must do
- both equations
- the first one only
- whichever is easier to solve
Answer
both equations — That's it. A pair that satisfies only one of them is simply not chosen.
How Maya teaches it
Your child tells Maya what they did in class. She teaches this topic at her desk, asks questions with tappable answers, and when the answer is wrong she explains why that answer was tempting instead of saying “try again”. She remembers what did not land and comes back to it.
Your child has it when they can: Say how a system's answer is checked.
How to help at home
The hard part of a system isn't the algebra — it's remembering that a solution has to answer two questions, not one. A child who finds x from the first equation often stops there, as if the second equation were just extra decoration.
Try this with two simple made-up rules: "the total of two numbers is 10" and "the first is 4 more than the second." Ask your child to guess a pair, then check it against both sentences separately, out loud, one at a time.
When your child offers a pair that fits only one equation, ask: "does that pair also work for the other sentence?" Don't say it's wrong — let them check and find the mismatch themselves.
A sign they've got it: after solving, they check their answer in both original equations without being asked, because they've internalized that a system's answer has two jobs, not one.
Questions parents ask
- Why does my child only check one equation?
- Solving the first equation feels like finishing the problem, especially once a number pops out. The habit of checking both takes deliberate practice, not more algebra.
- What's the easiest way to introduce a system of equations?
- Use two real-life clues about the same two numbers, like ages or amounts of money, and ask your child to find numbers that satisfy both clues at once, by guess-and-check first.
- Do I need to teach substitution and elimination both?
- Substitution is usually the easier first method: solve one equation for one unknown, then substitute it into the other. Elimination is a second tool worth adding once substitution feels solid.
- How does Maya teach systems of equations?
- Maya asks the child to check any guessed pair against both equations before showing a method, so 'must satisfy both' becomes a habit before it becomes a rule.
No card needed. The first lesson is free.
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