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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to solve two linked conditions by substitution.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Linear equations and substitution.
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 the system y = 2x + 1 and x + y = 10, then check the ordered pair in both equations.
Why this math matters
A system's solution must satisfy both equations at once; substitution replaces a variable by an equal expression. Use substitution when one condition already expresses one quantity directly in terms of another.
Set up the model
A useful answer starts with clear assumptions:
- Both equations refer to the same x and y.
- Solutions are real ordered pairs.
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.
Solve two linked conditions by substitution
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Solve the system y = 2x + 1 and x + y = 10, then check the ordered pair in both equations.
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
x + (2x + 1) = 10
Replace y in the second equation with its expression from the first.
Apply the relationship
3x + 1 = 10; x = 3; y = 2(3) + 1 = 7
Solve one variable, then use it to recover the other.
Check and interpret
(x,y) = (3,7); 7 = 2(3) + 1 and 3 + 7 = 10
Both original conditions hold, so the pair is the system's intersection.
The result
(x,y) = (3,7); 7 = 2(3) + 1 and 3 + 7 = 10
Both original conditions hold, so the pair is the system's intersection.
Common mistakes to catch
- Satisfying only one equation is not enough to solve a system.
- An ordered pair's x and y values cannot be exchanged without checking again.
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 y = x − 2 and x + y = 8.
Show a hint
Substitute x − 2 for y.
Reveal answer and explanation
(x,y) = (5,3)
2x − 2 = 8 gives x = 5, then y = 3.
Practice 2
Does (2,5) solve the original system?
Show a hint
Check each equation separately.
Reveal answer and explanation
No
It satisfies y = 2x + 1, but 2 + 5 = 7 rather than 10.
Take the idea with you
Use substitution when one condition already expresses one quantity directly in terms of another.
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: Cancel one variable by adding equations
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