Solve Simultaneous Equations: 2x + y = 9 and x = 5

Substitution Method with Known Variable

Solve the following equations:

{2x+y=9x=5 \begin{cases} 2x+y=9 \\ x=5 \end{cases}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the system of equations
00:09 Substitute the given X value, and solve for Y
00:25 Isolate Y
00:37 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equations:

{2x+y=9x=5 \begin{cases} 2x+y=9 \\ x=5 \end{cases}

2

Step-by-step solution

To solve this system of equations, we'll use the substitution method as follows:

  • Step 1: Identify the given information.
    We have two equations: {2x+y=9x=5 \begin{cases} 2x + y = 9 \\ x = 5 \end{cases}
  • Step 2: Substitute x=5x = 5 into the first equation.
    The equation becomes: 2(5)+y=9 2(5) + y = 9 which simplifies to: 10+y=9 10 + y = 9
  • Step 3: Solve for yy.
    Subtract 10 from both sides: y=910 y = 9 - 10 y=1 y = -1
  • Step 4: Verify the solution.
    Substituting x=5x = 5 and y=1y = -1 back into the first equation confirms the solution:
    2(5)+(1)=101=9 2(5) + (-1) = 10 - 1 = 9

Both equations are satisfied with x=5x = 5 and y=1y = -1.

Therefore, the solution to the system of equations is x=5,y=1 x = 5, y = -1 .

3

Final Answer

x=5,y=1 x=5,y=-1

Key Points to Remember

Essential concepts to master this topic
  • Substitution: Replace the known variable directly into the other equation
  • Technique: Substitute x = 5 into 2x + y = 9 to get 10 + y = 9
  • Check: Verify by substituting both values: 2(5) + (-1) = 9 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of substituting the given value
    Don't add x = 5 as a third equation or ignore it completely = wrong system solving! This misses the direct substitution opportunity. Always substitute the known value immediately into the other equation.

Practice Quiz

Test your knowledge with interactive questions

Solve the following equations:

\( \begin{cases} 2x+y=9 \\ x=5 \end{cases} \)

FAQ

Everything you need to know about this question

Why is this system so easy to solve?

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When one variable is already isolated (like x = 5), you can substitute it directly! This eliminates one variable immediately, making it a simple one-step substitution problem.

What if I get a negative answer for y?

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Negative answers are perfectly valid! In this case, y = -1 is correct. Don't assume answers must be positive - always trust your algebra and verify by substitution.

Do I need to use elimination method instead?

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Substitution is faster here! Since x is already solved, substitution takes just one step. Elimination would require unnecessary extra work for this type of system.

How do I check if my solution is right?

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Substitute both values into both original equations. For our answer: x = 5 ✓ (given), and 2(5) + (-1) = 9 ✓. Both equations must be satisfied!

What if the numbers don't work out nicely?

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Even if you get messy fractions or decimals, the method stays the same! Substitute the known value and solve for the remaining variable step by step.

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