determine whether the ordered pair is a solution to {2x+y=20 {6x-5y=12 (5,10)

We need to determine whether the ordered pair (5, 10) is a solution to the system of equations:

\[
\begin{aligned}
1. & \ 2x + y = 20 \\
2. & \ 6x - 5y = 12
\end{aligned}
\]

### Step 1: Check the first equation \( 2x + y = 20 \)

Substitute \( x = 5 \) and \( y = 10 \) into the first equation:

\[
2(5) + 10 = 20 \quad \Rightarrow \quad 10 + 10 = 20 \quad \Rightarrow \quad 20 = 20
\]

The first equation is satisfied.

### Step 2: Check the second equation \( 6x - 5y = 12 \)

Substitute \( x = 5 \) and \( y = 10 \) into the second equation:

\[
6(5) - 5(10) = 12 \quad \Rightarrow \quad 30 - 50 = 12 \quad \Rightarrow \quad -20 \neq 12
\]

The second equation is not satisfied.

### Conclusion:
Since the ordered pair (5, 10) does **not** satisfy the second equation, it is **not** a solution to the system of equations.

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Would you like further details on any step or have any other questions?

Here are 5 related questions you might find useful:
1. How do you solve systems of equations using substitution?
2. Can all systems of equations have a solution?
3. What is the graphical interpretation of this system of equations?
4. How do you solve systems of equations using the elimination method?
5. What does it mean when a system of equations has no solution?

**Tip:** If a system has no solution, it means the lines represented by the equations are parallel and never intersect!

determine whether the ordered pair is a solution to {2x + y = 20, 6x - 5y = 12} (5, 10)

Find out if the ordered pair (5, 10) is a solution to the system of equations 2x + y = 20 and 6x - 5y = 12. This step-by-step solution demonstrates checking both equations and explains key concepts in solving linear systems. Ideal for students in Grades 8-10.

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