Determine if the ordered triple is a solution to the system of equations.

Part:

Part 1-of 2
(a) (Choose one) a solution to the system of equations.

Ask by Conner Moran. in the United States

Mar 30,2025

Question

Determine if the ordered triple is a solution to the system of equations.

Part:

Part 1-of 2
(a) (Choose one) a solution to the system of equations.

Ask by Conner Moran. in the United States

Mar 30,2025

UpStudy AI · Accepted Answer

**Step 1: Substitute $$ (3, 0, 0) $$ into the first equation**

The first equation is 
$$
2x + y + 4z = 6.
$$
Substitute $$ x = 3 $$, $$ y = 0 $$, and $$ z = 0 $$:
$$
2(3) + 0 + 4(0) = 6 \quad \Rightarrow \quad 6 + 0 + 0 = 6.
$$
Thus, the first equation is satisfied.

**Step 2: Substitute $$ (3, 0, 0) $$ into the second equation**

The second equation is 
$$
x + 2y + 2z = 3.
$$
Substitute $$ x = 3 $$, $$ y = 0 $$, and $$ z = 0 $$:
$$
3 + 2(0) + 2(0) = 3 \quad \Rightarrow \quad 3 + 0 + 0 = 3.
$$
Thus, the second equation is satisfied.

**Step 3: Substitute $$ (3, 0, 0) $$ into the third equation**

The third equation is 
$$
-3x + y + 6z = -9.
$$
Substitute $$ x = 3 $$, $$ y = 0 $$, and $$ z = 0 $$:
$$
-3(3) + 0 + 6(0) = -9 \quad \Rightarrow \quad -9 + 0 + 0 = -9.
$$
Thus, the third equation is satisfied.

**Conclusion**

Since $$ (3, 0, 0) $$ satisfies all three equations, it is indeed a solution to the system of equations.

$$
\boxed{(3, 0, 0) \text{ is a solution to the system.}}
$$
$$ (3, 0, 0) $$ is a solution to the system of equations.

Determine if the ordered triple is a solution to the system of equations.

Part:

Part 1-of 2
(a) (Choose one) a solution to the system of equations.

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Answer

Solution

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Determine if the ordered triple is a solution to the system of equations. Part: Part 1-of 2 (a) (Choose one) a solution to the system of equations.

Upstudy AI Solution

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Solution

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Determine if the ordered triple is a solution to the system of equations.

Part:

Part 1-of 2
(a) (Choose one) a solution to the system of equations.