Linear, simultaneous and quadratic equations
Solving an equation means finding the values that make it true. The method changes with the type, but the principle — do the same to both sides — never does.
Lesson overview
What you'll learn in this lesson
Manipulate algebraic expressions, solve equations and interpret graphs of functions.
Key learning points
- • Linear equations and inequalities
- • Simultaneous equations
- • Quadratic equations
This lesson at a glance
- 30 minutes
- 20 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 20
Visual introductionPicture this
Linear, simultaneous and quadratic equations
Solving an equation means finding the values that make it true. The method changes with the type, but the principle — do the same to both sides — never does.
In a nutshell
Manipulate algebraic expressions, solve equations and interpret graphs of functions.
Learning cycle
Part 2 of 20
Learning cycle 1 of 2
Part 1 · Linear equations and inequalities
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 20
Learn
Linear equations and inequalities
Collect terms and use inverse operations. Inequalities work identically with one exception: multiplying or dividing by a negative reverses the sign. Represent the solution on a number line with an open circle for < or > and a filled circle for ≤ or ≥.
Reset break
Part 4 of 20
Pause
That's sitting 1 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 20
Learn
Simultaneous equations
Elimination: scale one or both equations so a variable has matching coefficients, then add or subtract. Substitution suits cases where one equation already gives a variable in terms of the other, and is essential when one equation is quadratic. Always substitute back to find the second variable and check both equations.
Quick check
Part 6 of 20
Quick check
Part 7 of 20
Reset break
Part 8 of 20
Pause
That's sitting 2 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 20
Learning cycle 2 of 2
Part 2 · Quadratic equations
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 20
Learn
Quadratic equations
Rearrange to the form ax² + bx + c = 0 first. Factorise where possible, since a product equals zero only when a bracket equals zero. Otherwise use the quadratic formula or complete the square. A negative discriminant means there are no real solutions, which is itself a valid answer.
Quick check
Part 11 of 20
Reset break
Part 12 of 20
Pause
That's sitting 3 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 13 of 20
Explore the idea
Part 14 of 20
Worked example
Worked answer: solve 3x + 2y = 16 and x − y = 2 (4 marks)
From the second equation, x = y + 2 (1). Substituting into the first: 3(y + 2) + 2y = 16, so 3y + 6 + 2y = 16 and 5y = 10 (1), giving y = 2 (1). Then x = 2 + 2 = 4 (1). Check in the first equation: 3(4) + 2(2) = 16, correct. Marks are lost most often by finding one variable and stopping.
Challenge round
Part 15 of 20
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Reset break
Part 16 of 20
Pause
That's sitting 4 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 17 of 20
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
Elimination: scale one or both ____ so a variable has matching coefficients, then add or subtract.
Challenge round
Part 18 of 20
Game · Recall cards
Dividing an inequality by −2 means you must
Card 1 of 4
Mastery quiz
Part 19 of 20
Marked quiz
End of lesson quiz: Linear, simultaneous and quadratic equations
4 questions, marked with the reasoning shown. No timer.
1. Dividing an inequality by −2 means you must
2. To solve x² − 5x + 6 = 0 by factorising, the brackets are
3. A quadratic with a negative discriminant has
4. Before using the quadratic formula you must
Lesson round-up
Part 20 of 20
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
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Points this lesson
0
Best run
0 in a row
Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 20 · Watch & discover