Let's address each part of the question.

Part a)

We are asked to create an equation that is equivalent to $x + y = 3$.

One simple way to manipulate this equation is to express $y$ in terms of $x$: $y = 3 - x$ This equation is equivalent to $x + y = 3$.

Part b)

Now, we will use the result from part a) to solve the simultaneous equations:

1. $2x + 3y = 7$
2. $x + y = 3$

From part a), we know that $y = 3 - x$. Let's substitute this into the first equation $2x + 3y = 7$:

$2x + 3(3 - x) = 7$ Simplifying: $2x + 9 - 3x = 7$ $-x + 9 = 7$ $-x = 7 - 9$ $-x = -2$ $x = 2$

Now that we know $x = 2$, substitute this into the equation $y = 3 - x$: $y = 3 - 2 = 1$

Solution:

The solution to the simultaneous equations is: $x = 2, \quad y = 1$

Do you have any questions or would you like further details?

Related Questions:

1. What are simultaneous equations, and how do you solve them algebraically?
2. Can we solve these equations using substitution or elimination? How do these methods differ?
3. How can we verify that $x = 2$ and $y = 1$ is the correct solution for both equations?
4. What other forms can the equation $x + y = 3$ take, and how do they affect the system?
5. What are the graphical interpretations of the simultaneous equations?

Tip:

Always substitute your solution back into both original equations to verify its accuracy!