Systems of equations – Grade 11 math lesson

Lesson 6 of 23 in the Grade 11 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 11 (ages 16–17) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.

Time: 45 minutes + 20 min homework
Grade: Grade 11 (ages 16–17)
You need: Paper, a pencil and this page
Graded: Instantly, with explanations

For parents: how to use this lesson

You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.

Read what your child will learn and the big ideas together.
Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
Finish with the exit ticket and the talk question: “What does it mean if the two lines never cross?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Adding when the signs mean you should subtract. Same signs: subtract. Different signs: add.
Finding x and forgetting y. Substitute back to find the other value, then check both equations.

Tip for home: Make up price puzzles with two unknown items.

What your child will learn

Learning goal: solve systems of equations by elimination, substitution and graphing.

Success looks like

I can solve by elimination.
I can solve by substitution.
I can solve using a graph.

Key words

system of equations: equations that are true at the same time
eliminate: remove one unknown
substitute: replace a letter with an expression
intersection: where two graphs cross

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Solve a puzzle: 2 coffees and 1 cake cost 7; 1 coffee and 2 cakes cost 8. Find each price.

The big ideas (for the adult)

A system of equations has the same two unknowns in each equation. The solution makes both true at once.

Elimination: make the coefficients of one letter match, then add or subtract the equations. Substitution: rearrange one and put it into the other.

On a graph, the solution is where the two lines cross.

The lesson, step by step

45 minutes in 5 parts
Part	Time	How it is checked
Starter: quick recall	5 min	Graded by Classfern
Teaching input	10 min	Not assessed, self-checked
Worked examples and guided practice	9 min	Not assessed, graded by Classfern
Independent practice	15 min	Graded by Classfern
Closure and exit ticket	6 min	Graded by Classfern, self-checked

Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.

The lesson

It runs here on the page. No sign-up and no names – progress is kept only in this browser.

Homework and practice at home

20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.

More practice

All Grade 11 math lessons and tests · Math Department

Curriculum

Common Core State Standards HSA.REI.C.8: “(+) Represent a system of linear equations as a single matrix equation in a vector variable.”

Common Core State Standards HSA.REI.C.9: “(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.