Learn with Amar
Teaching video
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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to cancel one variable by adding equations.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Signed subtraction and one-variable equations.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Solve 2x + 3y = 19 and 2x − y = 7 by eliminating x.
Why this math matters
Adding valid equations produces another true equation and can eliminate a variable with opposite coefficients. Choose a multiplication or addition step that creates opposite coefficients before starting elimination.
Set up the model
A useful answer starts with clear assumptions:
- Both equations must hold for the same pair.
- Subtract the entire second equation, including all its signs.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Cancel one variable by adding equations
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Solve 2x + 3y = 19 and 2x − y = 7 by eliminating x.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
(2x + 3y) − (2x − y) = 19 − 7
Matching x coefficients cancel when the equations are subtracted.
Apply the relationship
4y = 12; y = 3
Subtracting −y contributes another positive y.
Check and interpret
2x − 3 = 7 → x = 5; solution (5,3)
Checking gives 10 + 9 = 19 and 10 − 3 = 7.
The result
2x − 3 = 7 → x = 5; solution (5,3)
Checking gives 10 + 9 = 19 and 10 − 3 = 7.
Common mistakes to catch
- Subtract every term of the second equation, not only the matching variable term.
- Eliminating both variables can indicate dependent or inconsistent equations rather than a unique pair.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Solve x + y = 9 and x − y = 3.
Show a hint
Add the equations to eliminate y.
Reveal answer and explanation
(x,y) = (6,3)
2x = 12 gives x = 6; then y = 3.
Practice 2
For x + 2y = 8 and 3x + 6y = 24, how many real solutions are there?
Show a hint
Compare the second equation with three times the first.
Reveal answer and explanation
Infinitely many
The equations describe the same line; every point satisfying the first satisfies the second.
Take the idea with you
Choose a multiplication or addition step that creates opposite coefficients before starting elimination.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Decide whether a relation is a function
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