https://file.aiquickdraw.com/mathbot/file/1723426694914em2l76g1.jpg

To solve question 12 from the provided image, we need to solve the simultaneous equations using the method of substitution.

The equations provided are:
\[
4x + 5y = 25
\]
\[
2x + 3y = 14
\]

### Step 1: Solve one equation for one variable
Let's solve the second equation for \(x\):

\[
2x = 14 - 3y
\]
\[
x = \frac{14 - 3y}{2}
\]

### Step 2: Substitute this expression into the first equation
Substitute \(x = \frac{14 - 3y}{2}\) into the first equation \(4x + 5y = 25\):

\[
4\left(\frac{14 - 3y}{2}\right) + 5y = 25
\]

Simplify the equation:

\[
2(14 - 3y) + 5y = 25
\]

Distribute the 2:

\[
28 - 6y + 5y = 25
\]

Combine like terms:

\[
28 - y = 25
\]

### Step 3: Solve for \(y\)
\[
-y = 25 - 28
\]
\[
-y = -3
\]
\[
y = 3
\]

### Step 4: Substitute the value of \(y\) back into the expression for \(x\)
Substitute \(y = 3\) into the expression for \(x\):

\[
x = \frac{14 - 3(3)}{2}
\]
\[
x = \frac{14 - 9}{2}
\]
\[
x = \frac{5}{2}
\]
\[
x = 2.5
\]

### Final Answer
The solution to the system of equations is:
\[
x = 2.5, \quad y = 3
\]

Would you like further details or have any questions?

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Here are some related questions you might find helpful:

1. How would you solve the same system of equations using the elimination method?
2. What is the geometric interpretation of the solution to this system of equations?
3. How can you check if the solution obtained is correct?
4. What happens if the system of equations has no solution?
5. How can you solve the system if both equations are nonlinear?
6. How do you solve a system of three equations with three variables using substitution?
7. What are the differences between substitution and elimination methods in solving systems of equations?
8. Can you solve a system of equations graphically? How would it compare to algebraic methods?

**Tip:** When solving systems of equations, always check your solution by substituting the values back into the original equations.

Learn how to solve simultaneous equations using the substitution method with a detailed step-by-step solution. This problem covers key concepts in algebra, including simultaneous equations and the substitution method. Suitable for students in Grades 9-12.

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