Solve the following equations:
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Solve the following equations:
To solve this system of equations, we'll use the substitution method as follows:
Both equations are satisfied with and .
Therefore, the solution to the system of equations is .
Solve the following equations:
\( \begin{cases}
2x+y=9 \\
x=5
\end{cases}
\)
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.
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.
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.
Substitute both values into both original equations. For our answer: x = 5 ✓ (given), and 2(5) + (-1) = 9 ✓. Both equations must be satisfied!
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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