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) $$ (-12,-12) $$

Question

UpStudy AI · Accepted Answer

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)
The solution is $$ (8, 16) $$, which corresponds to choice C.

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) \( (-12,-12) \)