To solve the system of simultaneous equations:

1. $y - 7x + 18 = 0$
2. $3x + y - 2 = 0$

We can use either substitution or elimination. Let's solve by substitution.

Step 1: Solve one equation for $y$

From equation (2): $3x + y - 2 = 0 \quad \Rightarrow \quad y = 2 - 3x$

Step 2: Substitute $y = 2 - 3x$ into equation (1)

Substitute into equation (1): $(2 - 3x) - 7x + 18 = 0$ Simplifying: $2 - 3x - 7x + 18 = 0$ $2 - 10x + 18 = 0$ $20 - 10x = 0$ $10x = 20 \quad \Rightarrow \quad x = 2$

Step 3: Substitute $x = 2$ into $y = 2 - 3x$

$y = 2 - 3(2) = 2 - 6 = -4$

Final Solution:

$x = 2, \quad y = -4$

The solution to the simultaneous equations is $x = 2$ and $y = -4$.

Would you like more details or have any questions?

Related Questions:

1. What happens if you solve the system using the elimination method?
2. How do you verify the solution of simultaneous equations?
3. Can these equations be solved graphically, and what would the graphs look like?
4. How would you solve nonlinear simultaneous equations?
5. What are some applications of solving simultaneous equations in real life?

Tip: Always check your solution by substituting the values back into both original equations.