Two Unknowns, Two Scales

Lesson 4 of 12 · 7 min · Free, no account needed

What you will learn

Two equations with the same two unknowns make a system. Its solution makes both true at once.
Elimination: take one equation off the other so one unknown vanishes, then swap the answer back in.
On a graph, each equation is a line. The solution is where the two lines cross.

Two burgers and a shake cost $10. A burger and a shake cost $7. What does a burger cost?
Each scale is a receipt. Turn the dial to your bet.
Take scale B off scale A.
Drag scale B up onto scale A. What both receipts share comes off both pans.
Now the shake. Swap in what you know.
Tap the burger on scale B: it turns into $3 of weights.
Two scales are a system.
Two equations with the same two unknowns, 2b + s = 10 and b + s = 7, make a system of equations.
Elimination: take one equation off the other so one unknown vanishes: b = 3. Then swap it back in: s = 4.
Each equation is a line on the graph. The solution (3, 4) is the one point on both lines: where they cross.
Make the two receipts agree.
Turn the dial to try a burger price. Each receipt then says what a shake costs. Find the price where they agree.
Write your own menu puzzle.
Burgers cost $4 and fries $2. Fill two different receipts. A friend should be able to find both prices from them.
Game: beat Pip.
Pip guesses one price at a time. Drag B onto A, share if needed, then tap the item on B to swap in its price.
A model learns a line from examples. Solve it, or fit it?
Tap two points to solve for the line through them. Do it on the left, then try a few pairs on the right, then Fit.
Pip solves your menu.
Press Step to watch each move.

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