Today is rung 5 of 11 on this topic
Systems of equations
Can do: Solves systems by graphing, substitution and elimination, and knows what the solution represents.
Why it matters
Systems answer the question "when are these two things equal?", which is one of the most useful questions in applied maths.
What it looks like when it's wobbly
Can execute a method but has no idea the solution is the intersection point of two lines.
⏱️ Two-minute check
"Solve y = 2x + 1 and y = −x + 7. What does your answer mean on a graph?"
Solid looks like: (2, 5), and "the point where the two lines cross".
The full activity for this topic · 25 minutes
Which Plan Is Cheaper?
- 1Take two real plans — two phone tariffs, two gyms, two taxi firms.
- 2Write an equation for each and graph both on one grid.
- 3Find the crossing point and say what it means in words.
- 4Solve it algebraically and check it matches the graph.
- 5Answer the practical question: below what usage is plan A better?
If it's too hard
Graphing only, with integer solutions.
If it's too easy
Systems with no solution or infinitely many, and explaining what that means graphically.
Say this
"What is that point, in the actual situation? Not the numbers — the meaning."