Find the value of x and and band the substitution method.
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Find the value of x and and band the substitution method.
To solve the given system of linear equations using the substitution method, follow these steps:
From the second equation:
We can solve for as follows:
Substitute into the first equation:
Simplify and solve for :
- Distribute :
- Combine like terms:
- Add 80 to both sides:
- Divide by 49:
The expression for is:
- Substitute :
Therefore, the values that satisfy both equations in the system are and .
Solve the following equations:
\( \begin{cases}
2x+y=9 \\
x=5
\end{cases}
\)
Choose the equation where a variable has a coefficient of 1 (like x in x + 8y = 16). This avoids fractions and makes the algebra much simpler!
Take it one step at a time! When distributing -5(16 - 8y), write it as: -5 × 16 + (-5) × (-8y) = -80 + 40y. This helps avoid sign errors.
Always test your answer in both original equations. For x = 0, y = 2: Check -5(0) + 9(2) = 18 ✓ and 0 + 8(2) = 16 ✓
Yes! But it's usually harder because you'd get from the second equation, creating fractions. Always pick the easier variable to isolate first.
Go back and check your algebra! Common errors include: wrong signs when distributing, not combining like terms correctly, or arithmetic mistakes when dividing.
Yes! You could use elimination method by multiplying equations to eliminate variables. But substitution is often clearer when one variable has a coefficient of 1.
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