Question
3. Find the solution to the system of equations \( y=2 x \) \( x+y=24 \) (A) \( (12,12) \) (D) \( (16,8) \) (C) \( (8,16) \) (D) \( (-12,-12) \)
Ask by O'Quinn Cross. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is \( (8, 16) \), which corresponds to choice C.
Solution
To solve the system of equations:
1. \( y = 2x \)
2. \( x + y = 24 \)
**Step 1:** Substitute the expression for \( y \) from the first equation into the second equation.
\[
x + (2x) = 24
\]
**Step 2:** Combine like terms.
\[
3x = 24
\]
**Step 3:** Solve for \( x \).
\[
x = \frac{24}{3} = 8
\]
**Step 4:** Substitute \( x = 8 \) back into the first equation to find \( y \).
\[
y = 2(8) = 16
\]
**Solution:** \( (8, 16) \)
**Answer:** (8,16)
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Simplify this solution Mind Expander
To solve the system of equations, you can substitute the first equation into the second. Since \( y = 2x \), substitute \( y \) in the second equation: \( x + 2x = 24 \) This simplifies to: \( 3x = 24 \) Dividing both sides by 3 gives: \( x = 8 \) Now, substitute \( x \) back into the first equation to find \( y \): \( y = 2(8) = 16 \) So, the solution is \( (8, 16) \). Looks like the correct option is (C) \( (8,16) \)!
