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Let's verify whether the given pair of coordinates \((9, 1)\) is a solution to the simultaneous equations:

1. \(x + 3y = 12\)
2. \(5x - 2y = 43\)

We will substitute \(x = 9\) and \(y = 1\) into both equations and check if both hold true.

**Substitute in the first equation:**

\[
9 + 3(1) = 9 + 3 = 12
\]

The first equation is true.

**Substitute in the second equation:**

\[
5(9) - 2(1) = 45 - 2 = 43
\]

The second equation is also true.

Since both equations are satisfied, the point \((9, 1)\) **is** a solution to the given system of equations.

Do you want any further clarification? Here are 5 related questions to expand on this topic:

1. How do you solve simultaneous equations using substitution?
2. What is the graphical interpretation of solving simultaneous equations?
3. How can you solve simultaneous equations using elimination?
4. What happens when a system of equations has no solutions?
5. Can there be an infinite number of solutions to a system of simultaneous equations?

**Tip:** When solving simultaneous equations, always check the solution by substituting the values back into the original equations to verify accuracy.

A pair of simultaneous equations is given as below:
1. x + 3y = 12
2. 5x - 2y = 43
Verify whether the given pair of coordinates (9,1) is the solution to these simultaneous equations.

Learn how to verify if the coordinates (9,1) are the solution to a pair of simultaneous equations. This involves using algebraic substitution and checking if both equations hold true. Suitable for students in Grades 8-10.

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