Middle school maths, year 2 · unit 4
Simultaneous Linear Equations
Hens and rabbits: 7 animals and 20 legs in all. How many are hens? Two unknowns looks daunting, but there are two conditions as well, and that pins the answer down to one. We start by dragging a handle and counting.
Hens and rabbits
A board to adjustHens and rabbits are mixed together. All you know is how many animals there are and how many legs. Drag the gold handle to change the number of hens.
Take away what is the same
A board to arrangeA pouch is x and a box is y. Take away what the two equations have in common and only one kind is left. Drag one row onto the other.
Swap it in
A board to arrangeIf you know that one box is the same as two pouches, you can put two pouches where the box is in the equation. Drag the gold dashed group.
Two sentences, two equations
Joining boardTwo unknowns need two conditions. Turn the sentences into equations. Draw a line from each dot on the left to a dot on the right.
Try it yourself
Use what you found on the boards. The numbers change every time and the easy questions come first. Get three right and the lamp lights.
What to take away from this unit
- A linear equation in two unknowns, x and y, has many pairs of solutions. Two equations taken as a pair are simultaneous equations, and the x and y that make both true are their solution.
- Elimination: subtract or add the two equations side by side so that one letter disappears. If the coefficients differ, multiply both sides of one equation by the same number first.
- Substitution: when one equation looks like y = 2x, put that whole expression in place of y in the other.
- Either way, the aim is to get down to one letter. Find one value, then put it back into an original equation to find the other.
- For a problem in words, call the two things you want x and y and turn the two conditions into two equations. Check the answer against the sentence.